Question

The measure of spt is b. The measure of tpr in s five more than two times spt. The measure of qps is twelve less than eight times the last measure of spt. Find the measure of spt, tpr, and qps.

Answer 1

Hello.

In your question, we can see that the points Q, P, and R can be assumed that they are in a straight line, meaning that the angle measures will add up to 180 (think of half a circle, which is 360 degrees).

This means that every angle added up will add up to 180 degrees.

Meaning we can set up the below equation:

`(8b-12)+(b)+(2b+5)=180`

`8b-12+b+2b+5=180`

`11b-7=180`

`11b=187`

`b=17`

After finding
`b`, we can plug it back in to each expression for each angle measure.

∠QPS =
`8b-12=8(17)-12=124`

∠SPT =
`b=17`

∠TPR =
`2b+5=2(17)+5=39`

Hope this helps!