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Mars2501 [29]
3 years ago
9

Please help me out............................

Mathematics
1 answer:
Alina [70]3 years ago
3 0

Answer:

<h2>b = 15°</h2>

Step-by-step explanation:

If Pq = RQ then ΔPQR is the isosceles triangle. The angles QPR and PRQ have the same measures.

We know: The sum of the measures of the angeles in the triangle is equal 180°. Therefore we have the equation:

m∠QPR + m∠PRQ + m∠RQP = 180°

We have

m∠QPR = m∠PRQ and m∠RQP = 60°

Therefore

2(m∠QPR) + 60° = 180°       <em>subtract 60° from both sides</em>

2(m∠QPR) = 120°           <em>divide both sides by 2</em>

m∠QPR = 60° and m∠PRQ = 60°

Therefore ΔPRQ is equaliteral.

ΔPSR is isosceles. Therefore ∠SPR and ∠PRS are congruent. Therefore

m∠SPR = m∠PRS

In ΔAPS we have:

m∠SPR + m∠PRS + m∠RSP = 180°

2(m∠SPR) + 90° = 180°            <em>subtract 90° from both sides</em>

2(m∠SPR) = 90°             <em>divide both sides by 2</em>

m∠SPR = 45° and m∠PRS = 45°

m∠PRQ = m∠PRS + b

Susbtitute:

60° = 45° + b           <em>subtract 45° from both sides</em>

15° = b

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