Question

Find the value of b. Then find the angle measures of the pentagon.
6
(b +45)
(2b - 90)
90°
Sum of angle
measures: 540°

Answer 1

b + 3/2*b + b + 45 + 2b - 90 + 90 = 540
Or, 4b + 3b/2 + 45 = 540
Or, (8b+3b)/2 = 495
Or, 11b = 990
Or, b = 90
Now,
b+45 = 135
3/2*b = 135
2b - 90 = 90

Answer 2

The sum of angles in a shape is the addition of all angles in the shape. The value of b is 90.

From the attached pentagon, we have:

$Sum = 540^o$ -- sum of angles.

This means that:

$Sum = b + \frac 32b + 2b - 90 + 90 + b + 45$

Collect like terms

$Sum = b + \frac 32b + 2b + b- 90 + 90 + 45$

Evaluate like terms

$Sum = \frac{11}2b +45$

Substitute 540 for sum

$\frac{11}2b +45 = 540$

Collect like terms

$\frac{11}2b =-45 + 540$

$\frac{11}2b =495$

Isolate b

$b =495 \times \frac 2{11}$

$b =\frac {990}{11}$

$b =90^o$

Hence, the value of b is 90.

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