Answer:
m∠R = 72°
Step-by-step explanation:
As ΔPQR and ΔUVW are congruent, m∠R = m∠W.
Equate the expressions for the two angles and solve for x:
⇒ m∠R = m∠W
⇒ 10x - 18 = 8x
⇒ 10x - 18 + 18 = 8x + 18
⇒ 10x = 8x + 18
⇒ 10x - 8x = 8x + 18 - 8x
⇒ 2x = 18
⇒ 2x ÷ 2 = 18 ÷ 2
⇒ x = 9
Substitute the found value of x into the expression for m∠R:
⇒ m∠R = 10x - 18
⇒ m∠R = 10(9) - 18
⇒ m∠R = 90 - 18
⇒ m∠R = 72°
Therefore, m∠R = 72°.
