Question

Two angles are complementary angles if the sum of their measures is 90°. If the measure of the larger of the two complementary angles is 38° more than three times the measure of the smaller angle find the measures of the two angles

Answer 1

Answer:13 = Smaller Angle and 77 = Larger Angle

Step-by-step explanation: If the measure of the larger of the two complementary angles is 38 more than three times the measure of the smaller angle.

This tells us there are two angles.

• A larger one
• A smaller one
• We then look for which angle is being compared to the other one.

"38 more than three times the measure of the smaller angle"

• This tells us the smaller angle is the angle that being compared to thus it can be labeled as x.

• Let x = the smaller angle

To find the larger angle we must write out all the modifications. This angle is 38 more than. To represent 38 more than we can say +38 (more than indicating addition).

To represent three times the angle we can write 3x (three copies of x)

Thus...

• Let 3x+38 = the larger angle.

If both angles are complementary then they add to 90 so..

• x+3x+38=90
• We can combine like terms to get...
• 4x+38=90
• Subtract 38 and we get 4x=52 and then
• Divide by 4 on both sides nd we get x=13.
• We then can substitute x=13 in and get 13 and 77