NJGPA Applying Geometric Theorems 4

Question 1

In circle O, arc AB = 80° and arc CD = 40°. Two chords AC and BD intersect inside the circle at point E. What is the measure of angle AEB?

Accepted Answer

60°

Answer

The angle formed by two intersecting chords equals half the sum of the intercepted arcs: (80° + 40°) ÷ 2 = 60°.

Question 2

The sum of interior angles of a polygon is 1440°. How many sides does the polygon have?

Accepted Answer

10

Answer

Using (n − 2) × 180° = 1440°: n − 2 = 8, so n = 10 sides.

Question 3

Triangle RST is congruent to triangle UVW by SAS. RS = 8, ST = 10, and angle S = 45°. Which statement must be true?

Accepted Answer

UV = 8 and VW = 10

Answer

SAS congruence pairs RS↔UV and ST↔VW, so UV = 8, VW = 10, and angle V = 45°.

Question 4

Point P is outside a circle. Two secants from P intercept arcs of 100° and 40°. What is the measure of angle P?

Accepted Answer

30°

Answer

The angle formed by two secants from an external point = (difference of intercepted arcs) ÷ 2 = (100° − 40°) ÷ 2 = 30°.

Question 5

In parallelogram ABCD, angle A = 65°. What is the measure of angle C?

Accepted Answer

65°

Answer

Opposite angles of a parallelogram are congruent, so angle C = angle A = 65°.

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