Question

∠ RQS and ∠ TQS are a linear pair where m∠ RQS = 2x + 4 and m∠ TQS = 6x + 20

Answer 1

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Answer 2

Since the given angles are a linear pair, that means that they add up to 180 degrees (straight line). So we know that:
m∠ RQS + m∠ TQS = 180

Now let's answer the questions.
1. Solve for x
m∠ RQS + m∠ TQS = 180
2x + 4 + 6x + 20 = 180
2x + 6x + 4 + 20 = 180
(2 + 6)x + 24 = 180
8x + 24 = 180
8x = 156
x = 19.5

2. Find m∠ RQS and m∠ TQS
m∠ RQS = 2x + 4
m∠ RQS = 2*19.5 + 4
m∠ RQS = 39 + 4
m∠ RQS = 43


m∠ TQS = 6x + 20
m∠ TQS = 6*19.5 + 20
m∠ TQS = 117 + 20
m∠ TQS = 137

3. Show how you can check your answer.Verify that they do add up to 180.
So 43 + 137 = 180
This demonstrates that they do make up a linear pair.