Question

In a pair of complementary angles, the larger angle is six more than three times the smaller angle. the measures of the angles are

Answer 1

2 angles are Complementary, if the sum of their measures = 90°.

Let the 2 angles be A and B, and let their measures be m(A)=a, m(B)=b.

Let A be the larger angle.



"the larger angle is six more than three times the smaller angle."

can be 'translated' into algebra as: a = 6 + 3b

Also, since A and B are complementary, we have a+b=90°.


substitute a=6+3b in the second equation:

a+b=90°

(6°+3b+b)=90°


4b=90°-6°

b=84°/4=21°



Then, a = 90°-21°=69°


Answer: a= 69°, b=21°