11.) If RST is isosceles, find m S (15x-31) (9x+11)

m<S = 32°

Step-by-step explanation:

Recall that one if the properties of an isosceles triangle is that the base angles are congruent. This means the base angles (<R and <T) of ∆RST are equal.

Thus,

m<R = m<T

15x - 31 = 9x + 11 (substitution)

Collect like terms

15x - 9x = 31 + 11

6x = 42

Divide both sides by 6

x = 7

Find m<R and m<T

m<R = 15x - 31

Plug in the value of x

m<R = 15(7) - 31 = 74°

m<T = 9x + 11

Plug in the value of x

m<T = 9(7) + 11 = 74

✅m<S = 180 - (74 + 74) (sum of ∆)

m<S = 32°