Question

8-73.
For each diagram below, write and solve an equation for x

Answer 1

a.x=100 equation: 540=(125·2)+90+(2x)

b. x=3 equation: 6x+18=2x+30

Explanation:

a. We know that the interior angles of a pentagon have to equal 540 degrees.

So:

540=125+125+90 (hence the square) + x + x

simplify:

540=340+2x

simplify:

200=2x

x=100

b. Using the alternate exterior angles theorem we can say:
6x+18=2x+30

simplify:

4x+18=30

4x=12

x=3