Question

Angle PQT and Angle SQR are supplementary angles. If the measure of PQT is (3x+43)° and the measure of Angle SQR is (6x-25)°, what is the numeric measure of Angle PQT and Angle SQR?

Answer 1

∠PQT = 97°

∠SQR = 83°

Explanation:

Supplementary angles sum to 180°

⇒ ∠PQT + ∠SQR = 180°

Given:

• ∠PQT = (3x + 43)°
• ∠SQR = (6x - 25)°

Therefore:

⇒ (3x + 43) + (6x - 25) = 180

⇒ 3x + 6x + 43 - 25 = 180

⇒ 9x + 18 = 180

⇒ 9x = 162

⇒ x = 18

Substitute the found value of x into the expression for each angle:

⇒ ∠PQT = (3x + 43)°

⇒ ∠PQT = (3(18) + 43)°

⇒ ∠PQT = 97°

⇒ ∠SQR = (6x - 25)°

⇒ ∠SQR = (6(18) - 25)°

⇒ ∠SQR = 83°

Check

⇒ ∠PQT + ∠SQR = 97° + 83° = 180°