Question

1. consider triangle ghj with exterior angles shown. which two statements are true? a. the measure of ∠gjk is 85°. b. the measure of ∠gjk is 95°. c. the measure of ∠hjg is 45°. d. the measure of ∠hjg is 50°. e. the measure of ∠hjg is 85°.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
For \(\angle GJK\) (exterior angle of \(\triangle GHJ\)), the two non - adjacent interior angles are \(\angle H = 50^{\circ}\) and \(\angle HJG=45^{\circ}\).
So, \(\angle GJK=\angle H+\angle HJG\).

Step2: Calculate \(\angle GJK\)

Substitute \(\angle H = 50^{\circ}\) and \(\angle HJG = 45^{\circ}\) into the formula \(\angle GJK=\angle H+\angle HJG\).
\(\angle GJK=50^{\circ}+45^{\circ}=95^{\circ}\).

Answer:

B. The measure of \(\angle GJK\) is \(95^{\circ}\); C. The measure of \(\angle HJG\) is \(45^{\circ}\)