Answer:
x = 18
y = 6
Step-by-step explanation:
In triangle UTR, measures of all angles are equal (60°). (given)
Therefore, it is an equilateral triangle.
So, it's sides will also be equal.
In triangle TRS, m angle T = m angle S
So, RT = RS = 11 (sides opposite to the equal angles are equal)
In triangle URT,
UT = RT (sides of equilateral triangle)
x - 7 = 11
x = 11 + 7
x = 18
In triangle TRS,
m angle T = m angle S = 5y°
m angle R = 180° - 60° = 120° (Linear pair angles)
5y° + 5y° + 120° = 180°
10y° = 180° - 120°
10y° = 60°
y = 60/10
y = 6
