Q. If two angles are supplementary and one angle measures 40 degrees, what is the measure of the other angle?
A.
40 degrees
B.
50 degrees
C.
140 degrees
D.
180 degrees
Show solution
Solution
Supplementary angles add up to 180 degrees, so the other angle measures 180 - 40 = 140 degrees.
Correct Answer:
C
— 140 degrees
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Q. If two angles are vertical angles and one angle measures 120°, what is the measure of the other angle?
A.
60°
B.
90°
C.
120°
D.
180°
Show solution
Solution
Vertical angles are equal, so the other angle also measures 120°.
Correct Answer:
C
— 120°
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Q. If two angles of a triangle are 30 degrees and 70 degrees, what is the type of triangle based on its angles?
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. If two angles of a triangle are 30 degrees and 70 degrees, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
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. If two angles of a triangle are 30° and 60°, what is the measure of the third angle?
A.
30°
B.
60°
C.
90°
D.
120°
Show solution
Solution
The sum of angles in a triangle is 180°. Therefore, the third angle = 180° - 30° - 60° = 90°.
Correct Answer:
C
— 90°
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Q. If two angles of a triangle are 45 degrees and 45 degrees, what type of triangle is it?
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right
Show solution
Solution
A triangle with two equal angles is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. If two angles of a triangle are 45 degrees and 55 degrees, what is the measure of the third angle?
A.
80 degrees
B.
90 degrees
C.
100 degrees
D.
70 degrees
Show solution
Solution
Third angle = 180 - (45 + 55) = 80 degrees.
Correct Answer:
A
— 80 degrees
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Q. If two angles of a triangle are 45° and 55°, what is the measure of the third angle?
A.
80°
B.
90°
C.
100°
D.
70°
Show solution
Solution
Sum of angles in a triangle = 180°. Third angle = 180° - (45° + 55°) = 80°.
Correct Answer:
A
— 80°
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Q. If two angles of a triangle are 50 degrees and 60 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 sum of the angles in a triangle is 180 degrees. Third angle = 180 - 50 - 60 = 70 degrees.
Correct Answer:
C
— 70 degrees
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Q. If two angles of a triangle are 50 degrees and 70 degrees, what is the length of the third angle?
A.
30 degrees
B.
50 degrees
C.
60 degrees
D.
70 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (50 + 70) = 60 degrees.
Correct Answer:
A
— 30 degrees
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Q. If two angles of a triangle are 50 degrees and 70 degrees, what is the third angle?
A.
30 degrees
B.
40 degrees
C.
50 degrees
D.
60 degrees
Show solution
Solution
The third angle = 180 - (50 + 70) = 60 degrees.
Correct Answer:
B
— 40 degrees
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Q. If two angles of a triangle are 50 degrees and 70 degrees, what is the type of triangle based on its angles?
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. If two angles of a triangle are 50 degrees and 70 degrees, what type of triangle is it?
A.
Acute
B.
Right
C.
Obtuse
D.
Equilateral
Show solution
Solution
The sum of the angles is 120 degrees, which means the third angle is 60 degrees. All angles are less than 90 degrees, so it is an acute triangle.
Correct Answer:
A
— Acute
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Q. If two angles of a triangle are 50° and 60°, what is the measure of the third angle?
A.
70°
B.
80°
C.
90°
D.
100°
Show solution
Solution
The sum of the angles in a triangle is 180°. Therefore, the third angle is 180 - 50 - 60 = 70°.
Correct Answer:
B
— 80°
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Q. If two angles of a triangle are 70 degrees and 40 degrees, what is the length 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 = 180 - (70 + 40) = 70 degrees.
Correct Answer:
C
— 50 degrees
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Q. If two angles of a triangle are equal, what type of triangle is it?
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
Show solution
Solution
A triangle with two equal angles is called an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. If two angles of triangle ABC 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 angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (45 + 55) = 90 degrees.
Correct Answer:
B
— 90 degrees
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Q. If two chords AB and CD intersect at point E inside a circle, and AE = 3 cm, EB = 4 cm, what is the length of CE if ED = 6 cm?
A.
2 cm
B.
3 cm
C.
4 cm
D.
5 cm
Show solution
Solution
Using the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 4 = CE * 6, which gives CE = 2 cm.
Correct Answer:
B
— 3 cm
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Q. If two chords AB and CD intersect at point E inside a circle, and AE = 3 cm, EB = 4 cm, what is the length of segment CE if DE = 2 cm?
A.
6 cm
B.
8 cm
C.
5 cm
D.
7 cm
Show solution
Solution
By the intersecting chords theorem, AE * EB = CE * DE. Thus, 3 * 4 = CE * 2, which gives CE = 6 cm.
Correct Answer:
A
— 6 cm
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Q. If two chords AB and CD intersect at point E inside a circle, and AE = 3 cm, EB = 4 cm, what is the length of segment CE if ED = 6 cm?
A.
8 cm
B.
9 cm
C.
7 cm
D.
10 cm
Show solution
Solution
By the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 4 = CE * 6, leading to CE = 2 cm.
Correct Answer:
C
— 7 cm
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Q. If two chords AB and CD intersect at point E inside a circle, and AE = 3 cm, EB = 4 cm, what is the length of CE if DE = 2 cm?
A.
6 cm
B.
8 cm
C.
4 cm
D.
5 cm
Show solution
Solution
Using the intersecting chords theorem, AE * EB = CE * DE. Thus, 3 * 4 = CE * 2, which gives CE = 6 cm.
Correct Answer:
A
— 6 cm
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Q. If two chords AB and CD intersect at point E inside a circle, what is the relationship between the segments AE, EB, CE, and ED?
A.
AE * EB = CE * ED
B.
AE + EB = CE + ED
C.
AE = CE
D.
EB = ED
Show solution
Solution
According to the intersecting chords theorem, AE * EB = CE * ED.
Correct Answer:
A
— AE * EB = CE * ED
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Q. If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 4 cm, what is the length of CE if ED = 2 cm?
A.
6 cm
B.
8 cm
C.
4 cm
D.
5 cm
Show solution
Solution
Using the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 4 = CE * 2, which gives CE = 6 cm.
Correct Answer:
B
— 8 cm
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Q. If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 4 cm, what is the length of CE if ED = 6 cm?
A.
2 cm
B.
3 cm
C.
4 cm
D.
5 cm
Show solution
Solution
Using the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 4 = CE * 6, which gives CE = 2 cm.
Correct Answer:
A
— 2 cm
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Q. If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 5 cm, what is the length of CE if ED = 4 cm?
A.
6 cm
B.
8 cm
C.
12 cm
D.
10 cm
Show solution
Solution
According to the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 5 = CE * 4, which gives CE = 15/4 = 3.75 cm.
Correct Answer:
B
— 8 cm
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Q. If two chords AB and CD of a circle intersect at point E, and AE = 3 cm, EB = 5 cm, what is the length of segment CE if ED = 4 cm?
A.
6 cm
B.
8 cm
C.
12 cm
D.
10 cm
Show solution
Solution
According to the intersecting chords theorem, AE * EB = CE * ED. Thus, 3 * 5 = CE * 4, which gives CE = (15/4) = 3.75 cm.
Correct Answer:
B
— 8 cm
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Q. If two chords AB and CD of a circle intersect at point E, what is the relationship between AE, EB, CE, and ED?
A.
AE * EB = CE * ED
B.
AE + EB = CE + ED
C.
AE - EB = CE - ED
D.
AE / EB = CE / ED
Show solution
Solution
According to the intersecting chords theorem, AE * EB = CE * ED.
Correct Answer:
A
— AE * EB = CE * ED
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Q. If two chords AB and CD of a circle intersect at point E, which of the following is true?
A.
AE * EB = CE * ED
B.
AE + EB = CE + ED
C.
AE = CE
D.
EB = ED
Show solution
Solution
The theorem states that if two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal, i.e., AE * EB = CE * ED.
Correct Answer:
A
— AE * EB = CE * ED
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Q. If two chords in a circle are equal in length, what can be said about their corresponding arcs?
A.
They are equal
B.
One is longer
C.
They are perpendicular
D.
They intersect
Show solution
Solution
Equal chords subtend equal arcs in a circle, hence their corresponding arcs are equal.
Correct Answer:
A
— They are equal
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Q. If two chords in a circle are equal in length, what can be said about their distances from the center?
A.
They are equal
B.
They are unequal
C.
One is longer
D.
One is shorter
Show solution
Solution
In a circle, equal chords are equidistant from the center.
Correct Answer:
A
— They are equal
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