Question

In PQR,if mp = x -12 ,mq = 5x -27, and mr = 2x + 3, find x and the measure of each angle

Answer 1

Answer:

∠p= 15°  ,  ∠q = 108°   , ∠r = 57°

Step-by-step explanation:

Given that for triangle PQR,

∠P = x -12

∠q = 5x -27

∠r = 2x + 3

Now sum of three angles of a triangle = 180°

i.e ∠p + ∠q +∠r = 180°

So, (x -12)° + (5x-27)° + (2x + 3)° = 180°

or,  8x° -36° = 180°

Or x = $\frac{216}{8}$

So, x = 27°

∴ ∠P = 27° -12°  = 15°

  ∠q = (5 × 27)° -27° = 108°

  ∠r = (2 × 27)° + 3° = 57°

Hence ∠p= 15°  ,  ∠q = 108°   , ∠r = 57°     Answer