Question

HELP ME! In a complete sentence, describe the relationship between the three angles in the diagram below. Write and solve an equation to find the value of b and the measures of ∠QPS, ∠SPT, and ∠TPR.

Answer 1

b = 17

∠QPS = 124°

∠SPT = 17°

∠TPR = 39°

Explanation:

• The sum of the three angles shown is a linear angle, with a measure of 180°.

This fact can be used to write an equation:

(8b -12)° +b° +(2b+5)° = 180°

11b -7 = 180

11b = 187

b = 17

8b -12 = 8(17) -12 = 124

2b +5 = 2(17) +5 = 39

The value of b is 17.

The angle measures are ...

∠QPS = 124°

∠SPT = 17°

∠TPR = 39°