NJGPA Applying Geometric Theorems 2 — Questions and Answers
Question 1: Two parallel lines are cut by a transversal. One co-interior (same-side interior) angle measures 112°. What is the measure of the other co-interior angle?
- 68° (Correct answer)
- 112°
- 58°
- 78°
Correct answer: 68°
Co-interior angles are supplementary, so 180° − 112° = 68°.
Question 2: In triangle PQR, the exterior angle at vertex R measures 135°. If angle P = 60°, what is the measure of angle Q?
- 75° (Correct answer)
- 45°
- 95°
- 80°
Correct answer: 75°
An exterior angle equals the sum of the two non-adjacent interior angles: 135° = 60° + Q, so Q = 75°.
Question 3: A quadrilateral has three angles measuring 85°, 95°, and 110°. What is the fourth angle?
- 70° (Correct answer)
- 60°
- 80°
- 90°
Correct answer: 70°
The sum of interior angles of a quadrilateral is 360°, so the fourth angle = 360° − 85° − 95° − 110° = 70°.
Question 4: In a circle, a central angle intercepts an arc of 140°. What is the measure of an inscribed angle that intercepts the same arc?
- 70° (Correct answer)
- 140°
- 280°
- 35°
Correct answer: 70°
The Inscribed Angle Theorem states that an inscribed angle is half the central angle that intercepts the same arc: 140° ÷ 2 = 70°.
Question 5: Triangle ABC is isosceles with AB = AC. If angle A = 40°, what are the measures of angles B and C?
- 70° each (Correct answer)
- 60° each
- 80° each
- 50° each
Correct answer: 70° each
The base angles of an isosceles triangle are equal: (180° − 40°) ÷ 2 = 70° each.
Question 6: Two chords intersect inside a circle. One chord is divided into segments of 4 and 9. The other chord is divided into segments of 6 and x. What is x?
- 6 (Correct answer)
- 8
- 9
- 4
Correct answer: 6
By the Intersecting Chords Theorem, 4 × 9 = 6 × x, so x = 36 ÷ 6 = 6.
Question 7: In right triangle DEF with the right angle at E, DE = 9 and EF = 12. What is the length of DF?
- 15 (Correct answer)
- 21
- √225
- 18
Correct answer: 15
By the Pythagorean Theorem, DF = √(9² + 12²) = √(81 + 144) = √225 = 15.
NJGPA Applying Geometric Theorems 2
Two parallel lines are cut by a transversal.
One co-interior (same-side interior) angle measures 112°.
What is the measure of the other co-interior angle?