Finding measure of an angle when two angles are described in word problem. Angles are supplementary.

angle A and angle B are supplementary. The measure of angle B is equal to four times the complement of Angle A. What is the measure of Angle A?

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Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...

Hi Tiffany,

Angle A and angle B are supplementary

A+B=180° Equation 1

The measure of angle B is equal to four times the complement of angle A

The complement of angle A=90°-A

B=4(90°-A)

B=360°-4A

Substitute the value of B in equation 1

A+360°-4A=180°

-3A=-180°

A=60°

The measure of angle A=60°

B=360°-4A=360°-4(60°)=120°

The measure of angle B=120°

A + B = 180°

B = 4(90°-A)

4A + B = 360°

–A – B = –180°

–––––––––––––

3A = 180°

A = 60°

Thank you so much!!! I appreciate the quick response :)

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