Question

Instructions: Find the measure of x and y.

R
89°
E
Х°
81°
G
yo
F
=
Y
Check

Answer 1

m ∠x = 81° and m ∠y = 109°

Explanation:

m ∠R = 1/2 (arc REG) m ∠G = 1/2(arc REF)

89° = 1/2 (arc REG) 81 = 1/2(arc REF)

178° = arc REG 162° = arc REF

m ∠x = 1/2 arc REF

m ∠x = 1/2( 162°)

m ∠x = 81° or m ∠G = m ∠x because these to angles intersect the same arc, therefore they are equal.

Now the polygon interior angles = 360° and you know the measure of three of the four angles, solve for the missing angle .

m ∠R + m ∠x + m ∠y + m ∠G = 360°

89° + 81° + m ∠y + 89° = 360°

(89 + 81 + 81) + m ∠y = 360°

251° + m ∠y = 360°

m ∠y = 109°