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PLEASE HELP ME!!!

I don't understand...
If possible, please explain!

PLEASE HELP ME!!! I don't understand... If possible, please explain!-example-1

1 Answer

6 votes

Answer: 15 degrees

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Step-by-step explanation:

Triangle PQR and triangle PSR are isosceles since we are given PQ = RQ and PS = RS respectively.

From that, we can prove the base angles for each triangle are congruent. Specifically: angle SPR = angle SRP and angle QPR = angle QRP

Focus on triangle PQR. The vertex angle is 60, leaving 180-60 = 120 degrees left over to be split evenly between the two base angles. So each base angle is 120/2 = 60 degrees. We can conclude triangle PQR is equilateral as each angle is 60 degrees.

fact 1: angle QRP = 60 degrees

Through similar steps, angle SRP is 45 degrees. Any isosceles right triangle is always a 45-45-90 triangle.

fact 2: angle SRP = 45 degrees

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Use fact 1 and fact 2 to find the measure of b. We will subtract the angles like such

b = angle QRS

b = (angle QRP) - (angle SRP)

b = 60 - 45

b = 15 degrees

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