Question

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

Answer 1

x = 22

PQS = 112

SQR = 68

Explanation:

Straight angles equal to 180 degrees

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

9x - 18 = 180

9x = 198

x = 22

Answer 2

x = 22°

∠PQS = 112°

∠SQR = 68°

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°