Answer:
- b = 90
- left and right obtuse angles are 135°; others are 90°
Step-by-step explanation:
The problem tells you the sum of the angle measures is 540°. Add them up and solve the resulting 2-step linear equation.
Clockwise from top ...
(b) +(b +45) +(90) +(2b -90) +(3/2b) = 540
11/2b +45 = 540 . . . . . . collect terms
11/2b = 495 . . . . . . . . . subtract 45
b = (2/11)(495) = 90 . . . . multiply by the inverse of the b coefficient
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Now we know b=90. The angle measures, clockwise from top, are ...
90, 90+45 = 135, 90, 2(90)-90 = 90, (3/2)(90) = 135
That is, the obtuse angles are 135° and all the others are 90°.
