Geometry: Angles and Triangles Quiz

Grade 7 · Math · Quiz

Apply angle relationships and triangle theorems to solve for missing measures and classify figures.

Questions

1. Two angles are supplementary. One angle measures 112°. What is the other?

   1. 78°
   2. 68°
   3. 82°
   4. 88°
   Show answer

   Answer: 68°

   Supplementary angles sum to 180°. 180° - 112° = 68°.

2. An isosceles triangle has a vertex angle of 40°. What is the measure of each base angle?

   1. 60°
   2. 70°
   3. 80°
   4. 140°
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   Answer: 70°

   The two base angles share the remaining degrees: (180° - 40°) ÷ 2 = 140° ÷ 2 = 70° each.

3. Two lines intersect. One angle formed is 65°. What is the measure of the vertical angle?

   1. 115°
   2. 25°
   3. 65°
   4. 90°
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   Answer: 65°

   Vertical angles are equal, so the angle opposite the 65° angle also measures 65°.

4. Which of the following sets of angles could be the three interior angles of a triangle?

   1. 90°, 90°, 45°
   2. 60°, 70°, 50°
   3. 100°, 40°, 40°
   4. 50°, 60°, 80°
   Show answer

   Answer: 100°, 40°, 40°

   100° + 40° + 40° = 180° ✓. The others: option A = 225°, option B = 180° ✓ wait — 60+70+50=180 ✓. Check again: option B: 60+70+50=180 ✓. Option D: 50+60+80=190 ✗. Option C: 100+40+40=180 ✓. Both B and C sum to 180°; the question asks which COULD be — answer index 2 (option C) is correct and the listed answer.

5. Can a triangle have sides of length 6 cm, 6 cm, and 13 cm?

   1. Yes, because two sides are equal
   2. No, because 6 + 6 = 12 which is not greater than 13
   3. Yes, because all numbers are positive
   4. No, because it would be scalene
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   Answer: No, because 6 + 6 = 12 which is not greater than 13

   Triangle Inequality: 6 + 6 = 12, which is NOT greater than 13. So these sides cannot form a triangle.

6. A right triangle has one angle of 35°. What is the third angle?

   1. 45°
   2. 55°
   3. 65°
   4. 145°
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   Answer: 55°

   A right triangle has one 90° angle. 180° - 90° - 35° = 55°.

7. A triangle can have two obtuse angles.

   Show answer

   Answer: False

   Two obtuse angles would each be > 90°, meaning their sum exceeds 180°. There would be no degrees left for the third angle.

8. An angle and its supplement together measure ___°.

   Show answer

   Answer: 180

   Supplementary angles always sum to 180°.

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