Q. If two parallel lines are cut by a transversal, and one of the alternate interior angles is 45 degrees, what is the measure of the other alternate interior angle? (2020)
A.
45 degrees
B.
135 degrees
C.
90 degrees
D.
180 degrees
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Solution
Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, the other angle is also 45 degrees.
Correct Answer:
A
— 45 degrees
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Q. If two parallel lines are cut by a transversal, and one of the alternate interior angles is 75 degrees, what is the measure of the other alternate interior angle? (2020)
A.
75 degrees
B.
105 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, the other alternate interior angle is also 75 degrees.
Correct Answer:
A
— 75 degrees
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Q. If two parallel lines are cut by a transversal, what is the relationship between the alternate interior angles? (2020)
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are unequal
Show solution
Solution
When two parallel lines are cut by a transversal, the alternate interior angles are equal.
Correct Answer:
A
— They are equal
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Q. In a pair of alternate exterior angles, if one angle measures 120 degrees, what is the measure of the other angle? (2021)
A.
60 degrees
B.
120 degrees
C.
180 degrees
D.
90 degrees
Show solution
Solution
Alternate exterior angles are equal when two parallel lines are cut by a transversal. Therefore, if one angle is 120 degrees, the other alternate exterior angle is also 120 degrees.
Correct Answer:
B
— 120 degrees
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Q. In a pair of complementary angles, if one angle measures 30 degrees, what is the measure of the other angle?
A.
50 degrees
B.
60 degrees
C.
70 degrees
D.
80 degrees
Show solution
Solution
Complementary angles sum up to 90 degrees. Therefore, the other angle = 90 - 30 = 60 degrees.
Correct Answer:
B
— 60 degrees
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Q. In a pair of intersecting lines, if one angle measures 35 degrees, what is the measure of the adjacent angle?
A.
145 degrees
B.
35 degrees
C.
180 degrees
D.
90 degrees
Show solution
Solution
Adjacent angles on a straight line are supplementary. Therefore, the adjacent angle measures 180 - 35 = 145 degrees.
Correct Answer:
A
— 145 degrees
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Q. In a pair of supplementary angles, if one angle measures 110 degrees, what is the measure of the other angle? (2021)
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
Show solution
Solution
Supplementary angles sum up to 180 degrees. Therefore, the other angle is 180 - 110 = 70 degrees.
Correct Answer:
A
— 70 degrees
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Q. In a pair of vertically opposite angles, if one angle measures 120 degrees, what is the measure of the other angle? (2021)
A.
60 degrees
B.
120 degrees
C.
180 degrees
D.
90 degrees
Show solution
Solution
Vertically opposite angles are equal. Therefore, if one angle measures 120 degrees, the other angle also measures 120 degrees.
Correct Answer:
B
— 120 degrees
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Q. In a parallelogram, if the base is 8 cm and the height is 3 cm, what is the area? (2021)
A.
24 cm²
B.
30 cm²
C.
20 cm²
D.
18 cm²
Show solution
Solution
Area = base * height = 8 * 3 = 24 cm²
Correct Answer:
A
— 24 cm²
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Q. In a parallelogram, if the base is 8 cm and the height is 5 cm, what is the area? (2021)
A.
40 cm²
B.
30 cm²
C.
50 cm²
D.
20 cm²
Show solution
Solution
Area = base * height = 8 * 5 = 40 cm²
Correct Answer:
A
— 40 cm²
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Q. In a right triangle, if one angle is 30 degrees and the hypotenuse is 10 cm, what is the length of the side opposite the 30-degree angle? (2020)
A.
5 cm
B.
10 cm
C.
8 cm
D.
7 cm
Show solution
Solution
Opposite side = hypotenuse * sin(30°) = 10 * 1/2 = 5 cm.
Correct Answer:
A
— 5 cm
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Q. In a right triangle, if one angle is 45 degrees, what is the measure of the other non-right angle? (2021)
A.
30 degrees
B.
45 degrees
C.
60 degrees
D.
75 degrees
Show solution
Solution
In a right triangle, the sum of the angles is 180 degrees. If one angle is 45 degrees and the right angle is 90 degrees, the other angle must be 180 - (90 + 45) = 45 degrees.
Correct Answer:
B
— 45 degrees
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Q. In a triangle, if one angle is 45 degrees and the other is 45 degrees, what is the measure of the third angle? (2020)
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
The sum of the angles in a triangle is always 180 degrees. Therefore, if two angles are 45 degrees each, the third angle = 180 - (45 + 45) = 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. In a triangle, if one angle is 50 degrees and another is 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:
A
— 70 degrees
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Q. In a triangle, if one angle measures 40 degrees and another measures 70 degrees, what is the measure of the third angle?
A.
70 degrees
B.
80 degrees
C.
60 degrees
D.
50 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (40 + 70) = 70 degrees.
Correct Answer:
B
— 80 degrees
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Q. In a triangle, if one angle measures 45 degrees and another measures 55 degrees, what is the measure of the third angle? (2019)
A.
80 degrees
B.
90 degrees
C.
100 degrees
D.
110 degrees
Show solution
Solution
The sum of angles in a triangle is 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 one angle measures 50 degrees and another angle measures 60 degrees, what is the measure of the third angle? (2019)
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:
A
— 70 degrees
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Q. In a triangle, if one angle measures 50 degrees and another measures 60 degrees, what is the measure of the third angle? (2019)
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:
A
— 70 degrees
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Q. In a triangle, if one angle measures 60 degrees and another measures 80 degrees, what is the measure of the third angle? (2019)
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. Therefore, the third angle = 180 - 60 - 80 = 40 degrees.
Correct Answer:
A
— 40 degrees
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Q. In a triangle, if two sides are 7 cm and 10 cm, what is the maximum possible length of the third side? (2019)
A.
16 cm
B.
17 cm
C.
18 cm
D.
19 cm
Show solution
Solution
The maximum length of the third side = sum of the other two sides - 1 = 7 + 10 - 1 = 16 cm.
Correct Answer:
B
— 17 cm
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Q. In triangle ABC, if AB = AC and angle A = 40 degrees, what is the measure of angle B? (2023)
A.
70 degrees
B.
80 degrees
C.
60 degrees
D.
50 degrees
Show solution
Solution
In an isosceles triangle, angles opposite to equal sides are equal. Therefore, angle B = angle C = (180 - 40) / 2 = 70 degrees.
Correct Answer:
B
— 80 degrees
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Q. In triangle ABC, if angle A = 30 degrees and angle B = 60 degrees, what is the measure of angle C? (2021)
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (30 + 60) = 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the length of side DE if DF = 10 cm? (2023)
A.
5√2 cm
B.
10 cm
C.
10√2 cm
D.
20 cm
Show solution
Solution
In an isosceles right triangle, the sides opposite the 45-degree angles are equal. DE = DF/√2 = 10/√2 = 5√2 cm.
Correct Answer:
A
— 5√2 cm
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Q. In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the type of triangle? (2020)
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what type of triangle is DEF? (2021)
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle DEF, if DE = 12 cm, EF = 16 cm, and DF = 20 cm, what is the semi-perimeter? (2021)
A.
24 cm
B.
28 cm
C.
30 cm
D.
20 cm
Show solution
Solution
Semi-perimeter s = (12 + 16 + 20) / 2 = 48 / 2 = 24 cm.
Correct Answer:
B
— 28 cm
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Q. In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angle D is 90 degrees
Show solution
Solution
Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Thus, triangle DEF is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle GHI, if angle G = 30 degrees and side GH = 10 cm, what is the length of side HI if angle H = 60 degrees? (2023)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Using the sine rule, HI/sin(60) = GH/sin(30). Therefore, HI = (10 * sin(60)) / sin(30) = 10 * (√3/2) / (1/2) = 10√3 cm.
Correct Answer:
C
— 15 cm
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Q. In triangle GHI, if angle G = 90 degrees and GH = 9 cm, HI = 12 cm, what is the length of side GI? (2022)
A.
15 cm
B.
10 cm
C.
12 cm
D.
9 cm
Show solution
Solution
Using the Pythagorean theorem, GI = √(HI² - GH²) = √(12² - 9²) = √(144 - 81) = √63 = 15 cm.
Correct Answer:
A
— 15 cm
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Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the area of the triangle? (2019)
A.
120 cm²
B.
130 cm²
C.
140 cm²
D.
150 cm²
Show solution
Solution
Using Heron's formula, semi-perimeter s = (10 + 24 + 26) / 2 = 30. Area = √(s(s-a)(s-b)(s-c)) = √(30*20*6*4) = 120 cm².
Correct Answer:
A
— 120 cm²
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