Question

find the measure of Y in the given figure.

Answer 1

By using sum of two interior angle is equal to exterior angle
Angle q + angle p = angle x
Angle q +angle r =angle p
By angle sum property
Angle p +angle x + angle y =180
60° +60° + angle y = 180 °
Angle y = 180°-120°
= 60°

Answer 2

Angle P, Q and R = 60°(PQR is an equilateral triangle)
Angle x = 180°-60°=120°

Now in triangle PRS,
angle P + angle R + angle S = 180° (Angle sum property of a triangle) and
angle P = angle y ( angles
opposite to equal sides of a triangle are equal)
=> angle P + angle Y + angle X = 180°
=> 2(angle Y) + angle X = 180°
=> 2(angle Y) + 120° = 180°
=> 2(angle Y) = 180°-120°=60°

Angle Y = 60°÷2 = 30°