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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.

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

Answer :

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:

[tex](8b-12)+(b)+(2b+5)=180[/tex]

[tex]8b-12+b+2b+5=180[/tex]

[tex]11b-7=180[/tex]

[tex]11b=187[/tex]

[tex]b=17[/tex]

After finding [tex]b[/tex], we can plug it back in to each expression for each angle measure.

∠QPS = [tex]8b-12=8(17)-12=124[/tex]

∠SPT = [tex]b=17[/tex]

∠TPR = [tex]2b+5=2(17)+5=39[/tex]

Hope this helps!

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