For the figure shown below, find the value of the variable and the measures of the angles. x=
measure of angle P=
measure of angle Q=
measure of angle R=

x= 38°

measure of angle P= 58°

measure of angle Q= 84°

measure of angle R=38°

Step-by-step explanation:

Equations

The sum of the internal angles of a triangle is 180°. We are given the three angles as a function of x, thus:

2x - 18 + x + 46 + x = 180

Simplifying:

4x + 28 = 180

Subtracting 28:

4x = 180 - 28 = 152

x = 152/4 = 38

x = 38°

Angle P=2x-18=2*38-18=58°

Angle Q=x+46=38+46=84°

Angle R=x=38°

(3x-8) or (3x+8)

step-by-step explanation: