Answer: 15 degrees
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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
