Question

In ΔOPQ, m∠O = (3x+12)^{\circ}(3x+12)

∘
, m∠P = (4x+4)^{\circ}(4x+4)
∘
, and m∠Q = (x+12)^{\circ}(x+12)
∘
. Find m∠P

Answer 1

The measure of angle P is 80 degrees

Explanation:

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

In this problem we have that

`m\angle O+m\angle P+m\angle Q=180^o`

substitute the given values

`(3x+12)^o+(4x+4)^o+(x+12)^o=180^o`

solve for x

`(8x+28)=180`

`8x=180-28`

`8x=152`

`x=19`

Find the measure of angle P

`m\angle P=(4x+4)^o`

substitute the value of x

`m\angle P=(4(19)+4)=80^o`