Question

How do I solve for #23​

Answer 1

m<RQS = 43 deg

m<TQS = 137 deg

Explanation:

The measure of a straight angle is 180 deg.

The measures of angles RQS and TQS add up to 180 deg.

m<TQS + m<RQS = 180

6x + 20 + 2x + 4 = 180

8x + 24 = 180

8x = 156

x = 19.5

m<RQS = 2x + 4 = 2(19.5) + 4 = 43

m<TQS = 6x + 20 = 6(19.5) = 137

Answer 2

137

43

Explanation:

A straight line is another way of saying that the angle making the straight line always has 180 degrees. So the two angles in brown add up to 180 degrees.

6x + 20 + 2x + 4 = 180 Combine like terms on the left.

8x + 24 = 180 Subtract 24 from both sides.

8x + 24-24 = 180-24

8x = 156 Divide both sides by 8

8x/8 = 156/8 Do the division

x = 19.5

The two angles are

6x + 20 = 6*19.5 + 20 = 117 + 20 = 137

2x + 4 = 2*19.5 + 4 = 39 + 4 = 43

These do add to 180