NJGPA Applying Geometric Theorems 2

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?

Accepted Answer

68°

Answer

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?

Accepted Answer

75°

Answer

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?

Accepted Answer

70°

Answer

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?

Accepted Answer

70°

Answer

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?

Accepted Answer

70° each

Answer

The base angles of an isosceles triangle are equal: (180° − 40°) ÷ 2 = 70° each.

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

(NJGPA) New Jersey Graduation Proficiency Assessment Practice Test

NJGPA Applying Geometric Theorems 2