Answer:
∠ P = 29°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ PRS is an exterior angle of Δ RST , then
9x + 2 = 5x + 7 + 47
9x + 2 = 5x + 54 ( subtract 5x from both sides )
4x + 2 = 54 ( subtract 2 from both sides )
4x = 52 ( divide both sides by 4 )
x = 13
Then
∠ PRS = 9x + 2 = 9(13) + 2 = 117 + 2 = 119°
∠ PRS is also an exterior angle of Δ PRT , then
∠ P + ∠ Q = ∠ PRT , that is
∠ P + 90° = 119° ( subtract 90° from both sides )
∠ P = 29°
