Question

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=​

Answer 1

p=58

q=84

r=38

Explanation:

x+46+2x-18+x=180 degree ( angle sum property )

4x + 28 = 180 degree

4x = 180 - 28

4x = 152

x = 152 /4

x= 38

angle p = 2x -18 = 2 *38 -18 = 58 degree

angle q = x + 46 = 38 +46= 84 degree

angle r = x = 38 degree

Answer 2

x= 38°

measure of angle P= 58°

measure of angle Q= 84°

measure of angle R=​38°

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°