Angles Practice Test Question Answers (Elementary Geometry)
When the sum of the measures of two angles is 90°, the angles are called complementary angles. Each of them is called the complement of the other. Two angles are called adjacent angles if they have a common vertex
and a common arm but no common interior points. When the sum of the measures of two angles is 180°, the angles are called supplementary angles. Each of them is called a supplement of the other.
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Angles Practice Test
When two lines are intersected by a transversal, eight angles are formed. These angles can be classified as 4 interior angles, 4 exterior angles, 4 pairs of corresponding angles, 2 pairs of alternate interior angles, 2 pairs of alternate exterior angles, and two pairs of interior angles on the same side of the transversal.
1. In the following a pair of corresponding angles is
🔘 A. ∠1, ∠2
🔘 B. ∠2, ∠2
🔘 C. ∠3, ∠6
🔘 D. ∠4, ∠5
🔘 E. ∠3, ∠7
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Answer:∠3, ∠7
2. In the following figure AB||EF, ED||CB and ∠APE is 39°. Find ∠CQF.
🔘 A. ∠CQF= 28^{0}
🔘 B. ∠CQF= 39^{0}
🔘 C. ∠CQF= 93^{0}
🔘 D. ∠CQF= 139^{0}
🔘 E. ∠CQF= 141^{0}
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Answer:∠CQF= 141^{0} (Since ED||BC and AB is a transversal, so so ∠QBP = ∠APE
[Corresponding angles] or ∠QBP = 39° Now, AB||EF and BC is a transversal. Therefore, ∠FQB = ∠QBP [Alternate interior angles] Also, ∠CQF + ∠FQB = 180° [Linear pair] ∠CQF = 180° – 39°
3. Out of a pair of complementary angles, one is two-third of the other. Find the angles.
🔘 A. 18°
🔘 B. 36°
🔘 C. 54°
🔘 D. 90°
🔘 E. 180°
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Answer:B. 36° Let one angle be x. So, other angle = 90° – x Thus,
(2/3)× x = 90° – x or 5x = 270° or x=54° So, one angle = 54° and the other angle = 90° – 54°= 36°.
4. In the following figure CD intersects the line AB at F, ∠ CFB = 50° and ∠ EFA = ∠ AFD. Find the measure of ∠ EFC.
🔘 A. 50°
🔘 B. 80°
🔘 C. 90°
🔘 D. 120°
🔘 E. 180°
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Answer:B 80° Solution (∠CFB = ∠AFD (Vertically opposite angles) So, x = 50° But ∠EFA = ∠AFD which gives ∠EFA = 50° Now ∠CFB + ∠EFA + ∠EFC = 180° or, 50° + 50° + ∠EFC = 180° Thus, ∠EFC = 80°. [As AB is a straight line].
5. If the complement of an angle is 79°, then the angle will be of
🔘 A. 1°
🔘 B. 10°
🔘 C. 11°
🔘 D. 111°
🔘 E. 110°
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Answer: C C. 11°
6. In the following figure find the value of x is
🔘 A. 46°
🔘 B. 90°
🔘 C. 100°
🔘 D. 110°
🔘 E. 150°
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Answer:E. 150° (Sum of all angle about a point given in the figure are equal to 360° Then, 100o + 46o + 64o + x = 360°)
7. In the following figure if AB || CD, ∠ APQ = 50° and ∠PRD = 130°, then ∠ QPR is
🔘 A. 20°
🔘 B. 50°
🔘 C. 80°
🔘 D. 90°
🔘 E. 130°
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Answer: C. 80° (Hints: ∠APQ + ∠QPR = 130° )
8. If angle A and angle B are supplementary and the measure of angle A is 60°, then the measure of angle B is
🔘 A. 30°
🔘 B. 60°
🔘 C. 80°
🔘 D. 90°
🔘 E. 120°
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Answer:E. 120° (Hinsta P + Q = 180°)
9. The measure of an angle which is four times its supplement is
🔘 A. 36°
🔘 B. 90°
🔘 C. 110°
🔘 D. 120°
🔘 E. 144°
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Answer:E. 144° ( supplement angle = (180° – x) or x = 4 (180° – x)
10. In the following figure find the value of y
🔘 A. 10°
🔘 B. 20°
🔘 C. 33°
🔘 D. 45°
🔘 E. 60°
Show Answers
Answer:B. 20° (sol: Sum of all angle about a straight line given in the figure are equal to 180°
Then, 6y + y + 2y = 180° or 9y = 180°) or y=20°
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