Question

question 8 of 10
what is the value of y?

a. 54°
b. 108°
c. 72°
d. 36°

Explanation:

Step1: Identify triangle type

The triangle has two angles labeled \( y^\circ \) and one angle \( 72^\circ \), so it's isosceles (two equal angles).

Step2: Use triangle angle sum

Triangle angle sum is \( 180^\circ \). Let the equal angles be \( y \). So \( 72 + y + y = 180 \).

Step3: Solve for \( y \)

Simplify: \( 72 + 2y = 180 \). Subtract 72: \( 2y = 108 \). Divide by 2: \( y = 54 \). Wait, no—wait, maybe I misidentified. Wait, if two angles are \( y \), then \( 2y + 72 = 180 \) → \( 2y = 108 \) → \( y = 54 \)? But wait, maybe the triangle has two angles \( y \) and one \( 72 \). Wait, no, the diagram: the top angle is \( y \), bottom left \( 72 \), bottom right \( y \). So two angles \( y \), one \( 72 \). So sum: \( y + y + 72 = 180 \) → \( 2y = 108 \) → \( y = 54 \). Wait, but option A is \( 54^\circ \). Wait, but maybe I made a mistake. Wait, no—wait, maybe the triangle is isosceles with two angles \( y \), so the two base angles? Wait, no, the top angle is \( y \), bottom two: left \( 72 \), right \( y \). So that would mean two angles: top \( y \), right \( y \), left \( 72 \). So sum: \( y + y + 72 = 180 \) → \( 2y = 108 \) → \( y = 54 \). So answer is A.

Answer:

A. \( 54^\circ \)