Answer:
m ∠x = 81° and m ∠y = 109°
Step-by-step 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°
