Question

Consider the attached diagram, where ∠PQR is a straight angle.

Answer 1

Answer:

x = 22°

∠PQS = 112°

∠SQR = 68°

Step-by-step explanation:

        Since ∠PQR is a straight angle, it is equal to 180°. This means that ∠PQS and ∠SQR added together is also equal to 180°.

        ∠PQS + ∠SQR = 180°

        (6x - 20) + (3x + 2) = 180°

        6x + 3x + 2 - 20 = 180°

        9x - 18 = 180°

        9x = 198°

                 x = 22

        Now, we can substiute x into ∠PQS and ∠SQR.

        ∠PQS

        (6(22) - 20)

                 ∠PQS = 112°

        ∠SQR

        (3x + 2)

        (3(22) + 2)

                 ∠SQR = 68°

Answer 2

Answer:

x = 22

PQS = 112

SQR = 68

Step-by-step explanation:

Straight angles equal to 180 degrees

(6x - 20) + (3x + 2) = 180

9x - 18 = 180

9x = 198

x = 22