R is the interior of angle TUV. The measure of RUV=30degrees, the measure of TUV=3x+16, and the measure of TUR=x+10. Find x and the measure of TUV.

Given

R is the interior of ∠ TUV.

m∠ RUV=30degrees, m∠ TUV=3x+16, and m∠ TUR=x+10.

Find the value of x and the m ∠TUV.

To proof

As given in the question

m ∠TUV=3x+16, and m ∠TUR=x+10

thus

m∠ RUV = m∠ TUV - m∠ TUR

= 3x + 16 - x - 10

= 2x + 6

As given

m ∠RUV=30°

compare both the values

we get

30 = 2x + 6

24 = 2x

12 = x

put this value in the m ∠TUV = 3x+16

m ∠TUV = 12 * 3 + 16

= 52°

Hence proved