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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?

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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2 Answers

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°

Comments

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?

A + B = 180°

B = 4(90°-A)

4A + B = 360°
–A – B = –180°
–––––––––––––
3A = 180°

A = 60°

Comments