Question

4. If mZRST = (12x - 1)º, mZRSU = (9x - 15),

and mZUST = 53°, find each measure.
x=
mZRST =
mZRSU =

Answer 1

mZRST = 155°, mZRSU = 102°

Explanation:

Given that mZRST = (12x - 1)º, mZRSU = (9x - 15), and mZUST = 53°.

We know that mZRSU + mZUST = mZRST (since S is a common point)

So, (9x - 15)º + 53° = (12x - 1)º

Expanding the brackets we have

9x - 15 + 53 = 12x - 1

collecting like terms, we have

53 - 15 + 1 = 12x - 9x

54 - 15 = 3x

39 = 3x

Dividing through by 3, we have

x = 39/3

x = 13°

So, mZRST = (12x - 1)º

= 12(13) - 1

= 156 - 1

= 155°

So, mZRST = 155°

mZRSU = (9x - 15),

= 9(13) - 15

= 117 - 15

= 102°

So, mZRSU = 102°