Question

Find the values of x and y in the diagram.

Answer 1

x = 18

y = 6

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