Question

Find an angle such that the measure of its supplement is 10 degrees less than 3 times the measure of its complement.​

Answer 1

Provided:-

• Supplement is 10° less than 3 times the measure of its complement.

To Find:-

• An angle

Solution:-

Two angles are supplementary if their measures add up to 180 degrees. Two angles are complementary if their measures add up to 90 degrees.

As we know:

Let x = the angle

Then 90 - x = its complement

And 180 - x = its supplement

From the problem, we know that:

→ 180 - x = 3(90 - x) - 10

→ 180 - x = 270 - 3x - 10

→ 180 - x = 260 - 3x

→ 180 + 2x = 260

→ 2x = 80

→ x = 40

Hence, The angle is 40 degrees.

Verification:-

• Complementary angle = 90 - 40 = 50
• Supplementary angle = 180 - 40 = 140

According to the question:

Supplementary angle is 10 less than thrice of complementary angle:-

→ 3 × 50 - 10 = 150 - 10 = 140

LHS = RHS

Hence Verified!