Q. In a triangle, if one angle is 90 degrees and the other two angles are 45 degrees each, what is the area if the length of each leg is 5 cm?
A.
12.5 cm²
B.
25 cm²
C.
20 cm²
D.
15 cm²
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 5 * 5 = 12.5 cm².
Correct Answer:
B
— 25 cm²
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Q. In a triangle, if one angle is 90 degrees and the other two angles are 45 degrees each, what is the area if the legs are 5 cm each?
A.
12.5 cm²
B.
25 cm²
C.
20 cm²
D.
15 cm²
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 5 * 5 = 12.5 cm².
Correct Answer:
A
— 12.5 cm²
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Q. In a triangle, if one angle measures 30 degrees and the other measures 60 degrees, what is the measure of the third angle?
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
The third angle can be found by subtracting the sum of the other two angles from 180 degrees: 180 - (30 + 60) = 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. In a triangle, if one angle measures 40 degrees and another angle measures 60 degrees, what is the measure of the angle formed by a transversal intersecting the line parallel to the base of the triangle?
A.
40 degrees
B.
60 degrees
C.
80 degrees
D.
100 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. The third angle is 180 - (40 + 60) = 80 degrees. The angle formed by the transversal is equal to this angle.
Correct Answer:
C
— 80 degrees
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Q. In a triangle, if one angle measures 40 degrees and another angle measures 60 degrees, what is the measure of the third angle?
A.
80 degrees
B.
100 degrees
C.
60 degrees
D.
40 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 40 - 60 = 80 degrees.
Correct Answer:
A
— 80 degrees
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Q. In a triangle, if one angle measures 40 degrees and another angle measures 70 degrees, what is the measure of the third angle?
A.
70 degrees
B.
40 degrees
C.
50 degrees
D.
60 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 40 - 70 = 70 degrees.
Correct Answer:
C
— 50 degrees
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Q. In a triangle, if one angle measures 40 degrees and another measures 60 degrees, what is the measure of the third angle?
A.
80 degrees
B.
100 degrees
C.
60 degrees
D.
40 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 40 - 60 = 80 degrees.
Correct Answer:
A
— 80 degrees
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Q. In a triangle, if one angle measures 50 degrees and another angle measures 60 degrees, what is the measure of the angle formed by a line parallel to one side of the triangle and the extension of the other side?
A.
70 degrees
B.
50 degrees
C.
60 degrees
D.
130 degrees
Show solution
Solution
The third angle of the triangle is 70 degrees. The angle formed by the parallel line and the extension of the other side is equal to this angle due to the Corresponding Angles Postulate.
Correct Answer:
A
— 70 degrees
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Q. In a triangle, if one angle measures 50 degrees and the other two angles are equal, what is the measure of each of the equal angles?
A.
65 degrees
B.
70 degrees
C.
80 degrees
D.
90 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Let x be the measure of each equal angle: 50 + 2x = 180, so 2x = 130, thus x = 65 degrees.
Correct Answer:
B
— 70 degrees
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Q. In a triangle, if one angle measures 60 degrees and the other measures 70 degrees, what is the measure of the third angle?
A.
50 degrees
B.
60 degrees
C.
70 degrees
D.
80 degrees
Show solution
Solution
The third angle can be found by subtracting the sum of the other two angles from 180 degrees: 180 - (60 + 70) = 50 degrees.
Correct Answer:
D
— 80 degrees
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Q. In a triangle, if one angle measures 70 degrees and another measures 50 degrees, what is the measure of the third angle?
A.
60 degrees
B.
70 degrees
C.
80 degrees
D.
90 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 70 - 50 = 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. In a triangle, if one angle measures 70 degrees and the other measures 50 degrees, what is the measure of the third angle?
A.
60 degrees
B.
70 degrees
C.
80 degrees
D.
90 degrees
Show solution
Solution
The sum of the angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 70 - 50 = 60 degrees.
Correct Answer:
C
— 80 degrees
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Q. In a triangle, if the lengths of the sides are 7 cm, 24 cm, and 25 cm, is it a right triangle?
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angles are known
Show solution
Solution
To determine if it is a right triangle, we can use the Pythagorean theorem. Here, 25² = 7² + 24², which simplifies to 625 = 49 + 576, thus 625 = 625. Therefore, it is a right triangle.
Correct Answer:
A
— Yes
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Q. In a triangle, if the lengths of the sides are 7 cm, 24 cm, and 25 cm, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Scalene
Show solution
Solution
This triangle is a right triangle because 7² + 24² = 25² (49 + 576 = 625).
Correct Answer:
C
— Right
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Q. In a triangle, if the lengths of two sides are 5 cm and 12 cm, what is the maximum possible length of the third side?
A.
16 cm
B.
17 cm
C.
18 cm
D.
19 cm
Show solution
Solution
By the triangle inequality theorem, the maximum length of the third side is less than the sum of the other two sides: 5 + 12 = 17 cm.
Correct Answer:
B
— 17 cm
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Q. In a triangle, if the lengths of two sides are 7 cm and 24 cm, what is the minimum possible length of the third side?
A.
1 cm
B.
17 cm
C.
18 cm
D.
31 cm
Show solution
Solution
By the triangle inequality theorem, the length of the third side must be greater than the difference of the other two sides. Therefore, the minimum length = 24 - 7 = 17 cm.
Correct Answer:
B
— 17 cm
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Q. In a triangle, if the lengths of two sides are 8 cm and 15 cm, what is the maximum possible length of the third side?
A.
22 cm
B.
23 cm
C.
24 cm
D.
25 cm
Show solution
Solution
The maximum length of the third side is less than the sum of the other two sides: 8 + 15 = 23 cm, so the maximum possible length is 22 cm.
Correct Answer:
A
— 22 cm
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Q. In a triangle, if two angles are 45 degrees and 55 degrees, what is the measure of the third angle?
A.
80 degrees
B.
90 degrees
C.
100 degrees
D.
110 degrees
Show solution
Solution
The sum of the angles in a triangle is always 180 degrees. Therefore, the third angle = 180 - (45 + 55) = 180 - 100 = 80 degrees.
Correct Answer:
B
— 90 degrees
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Q. In a triangle, if two angles are 45 degrees and 55 degrees, what is the measure of the angle formed by a line parallel to one side of the triangle and the extension of the other side?
A.
80 degrees
B.
45 degrees
C.
55 degrees
D.
100 degrees
Show solution
Solution
The third angle of the triangle is 80 degrees. The angle formed by the parallel line and the extension of the other side is equal to this angle due to the Corresponding Angles Postulate.
Correct Answer:
A
— 80 degrees
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Q. In a triangle, if two angles are 45 degrees and 55 degrees, what is the third angle?
A.
80 degrees
B.
90 degrees
C.
100 degrees
D.
110 degrees
Show solution
Solution
The sum of the angles in a triangle is always 180 degrees. Therefore, the third angle = 180 - (45 + 55) = 180 - 100 = 80 degrees.
Correct Answer:
B
— 90 degrees
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Q. In a triangle, if two angles are 45 degrees and 55 degrees, what type of triangle is it?
A.
Acute
B.
Right
C.
Obtuse
D.
Equilateral
Show solution
Solution
Since all angles are less than 90 degrees, the triangle is acute.
Correct Answer:
A
— Acute
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Q. In a triangle, if two angles are 45 degrees each, what is the measure of the third angle?
A.
45 degrees
B.
60 degrees
C.
90 degrees
D.
75 degrees
Show solution
Solution
The sum of the angles in a triangle is always 180 degrees. If two angles are 45 degrees each, the third angle is 180 - (45 + 45) = 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. In a triangle, if two angles are 50 degrees and 60 degrees, what is the measure of the third angle?
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - (50 + 60) = 70 degrees.
Correct Answer:
B
— 80 degrees
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Q. In a triangle, if two angles are equal and one measures 50 degrees, what is the measure of the third angle?
A.
50 degrees
B.
80 degrees
C.
100 degrees
D.
60 degrees
Show solution
Solution
Let the equal angles be x. Then, 2x + 50 = 180. Solving gives x = 65 degrees, so the third angle is 180 - 2(50) = 80 degrees.
Correct Answer:
B
— 80 degrees
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Q. In a triangle, if two angles are equal and the third angle measures 40 degrees, what is the measure of each of the equal angles?
A.
70 degrees
B.
40 degrees
C.
20 degrees
D.
60 degrees
Show solution
Solution
Let each equal angle be x. The sum of angles in a triangle is 180 degrees, so 2x + 40 = 180. Thus, 2x = 140, giving x = 70 degrees.
Correct Answer:
A
— 70 degrees
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Q. In a triangle, if two angles measure 45 degrees and 55 degrees, what is the measure of the third angle?
A.
80 degrees
B.
90 degrees
C.
100 degrees
D.
110 degrees
Show solution
Solution
The sum of the angles in a triangle is always 180 degrees. Therefore, the third angle = 180 - (45 + 55) = 80 degrees.
Correct Answer:
B
— 90 degrees
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Q. In a triangle, if two angles measure 45 degrees each, what is the measure of the third angle?
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle is 180 - 45 - 45 = 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. In a triangle, if two angles measure 45 degrees each, what type of triangle is it?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
A triangle with two equal angles is an isosceles triangle. Since two angles measure 45 degrees, it is isosceles.
Correct Answer:
B
— Isosceles
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Q. In a triangle, if two angles measure 50 degrees and 60 degrees, what is the measure of the third angle?
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (50 + 60) = 70 degrees.
Correct Answer:
B
— 80 degrees
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Q. In a triangle, if two sides are 7 units and 24 units, what is the maximum possible length of the third side?
A.
30 units
B.
25 units
C.
31 units
D.
32 units
Show solution
Solution
The maximum length of the third side is less than the sum of the other two sides: 7 + 24 = 31 units.
Correct Answer:
B
— 25 units
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