Question

If rst is isosceles, find angle s

Answer 1

∠ S = 32°

Explanation:

the sides RS and ST are congruent (equal) , as indicated by the dashes through the sides.

Then Δ RST is isosceles with base angles R and T being congruent , then

∠ R = ∠ T ( substitute values )

15x - 31 = 9x + 11 ( subtract 9x from both sides )

6x - 31 = 11 ( add 31 to both sides )

6x = 42 ( divide both sides by 6 )

x = 7

Then

∠ T = 9x + 11 = 9(7) + 11 = 63 + 11 = 74° = ∠ R

the sum of the 3 angles in the triangle = 180° , that is

∠ S + ∠ R + ∠ T = 180° ( substitute 74 for R and T )

∠ S + 74° + 74° - 180°

∠ S + 148° = 180° ( subtract 148° from both sides )

∠ S = 32°