Answer:
Hence, m∠R=95°.
Explanation:
We are given that ΔABC is similar to the ΔRST i.e. ΔABC~ΔRST.
Aslo m∠A=6x+17, m∠B=3x+9, and m∠C=37
We know that sum of all the angles of a triangle is 180°.
⇒ ∠A+∠B+∠C=180
⇒ 6x+17+3x+9+37=180
⇒ 9x+63=180 (As 6x+3x=9x and 17+9+37=63)
⇒ 9x=180-63
⇒9x=117
⇒ x=13. (on dividing both side by 9)
Hence m∠A=6x+17=6×13+17=95°
m∠B=3x+9=3×13+9=48°
m∠C=37°
Also as ΔABC~ΔRST so this implies m∠R=m∠A=95°
Hence, m∠R=95°.