Question

Find the length of UT and the measure of angle R

A. UT= 104, m angle R=113
B. UT= 104, m angle R=126
C. UT= 112, m angle R=126
D. UT= 126, m angle R=104

Answer 1

B

Explanation:

∠R = ∠ U

10y - 14 = 5y + 56

Add 14 to both sides

10y - 14 + 14 = 5y + 56 + 14

10y = 5y + 70

Subtract 5y from both sides

10y -5y = 5y + 70 - 5y

5y = 70

y = 70/5

y = 14

∠R = 10y - 14 = 10*14 -14 = 140 - 14 = 126

∠R 126

RQ = UT

14x - 36 = 2x + 84

Add 36 to both sides

14x - 36 + 36 = 2x + 84 + 36

14x = 2x + 120

Subtract 2x from both sides

14x - 2x = 2x + 120 - 2x

12x = 120

x = 120/12

x = 10

UT = 2x +84 = 2*10 + 84 = 20 + 84 = 104

UT = 104