Question

ABC~RST with m<A=6x+17, m<3x+9, and m<C=37. Find the measure of R

Answer 1

Answer:

Hence, m∠R=95°.

Step-by-step 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°.