Question

Find the value of b. Then find the angle measures of the pentagon.

Answer 1

b = 90

Explanation:

Sum the interior angles of the pentagon and equate to 540

Starting from the top and going clockwise

b + b + 45 + 90 + 2b - 90 +
`(3)/(2)` b = 540 ← simplify left side

`(11)/(2)` b + 45 = 540 ( multiply through by 2 to clear the fraction )

11b + 90 = 1080 ( subtract 90 from both sides )

11b = 990 ( divide both sides by 11 )

b = 90

Thus

b + 45 = 90 + 45 = 135

2b - 90 = 2(90) - 90 = 180 - 90 = 90

`(3)/(2)` b =
`(3)/(2)` × 90 = 135

The angle measure from the top clockwise are

90°, 135°, 90°, 90°, 135°