A parallelogram has two adjacent angles that are supplementary. One angle is 55° less than the other. What is the measure of the smaller angle?

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01-03-2021
Mathematics

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A parallelogram has two adjacent angles that are supplementary. One angle is 55° less than the other. What is the measure of the smaller angle?

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lsummers2234 lsummers2234 · Answer 1 · 2021-03-01T23:20:39+01:00

lsummers2234 lsummers2234

01-03-2021

a parallelogram has 4 angles each adding up to 360°. two pairs of angles will be the same so angle A and angle B. Angle A=B-55 and 2A+2B=360 substitute A
2(B-55)+2B=360
distributive property: 2B-110+2B=360
add over 110 and combine like terms: 4B=450
divide by 4: B=112.5
substitute B into A=B-55: A=112.5-55=57.5
the smaller angle is 57.5°

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