Question

pqrs is an isosceles trapezoid with bases sr and pq, m∠p = 3x + 5, and m∠q = 6x - 10. find m∠p.

Explanation:

Step1: Use property of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal. So, \(m\angle P=m\angle Q\).
Set up the equation \(3x + 5=6x-10\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(5 = 6x-3x - 10\), which simplifies to \(5=3x - 10\).
Add 10 to both sides: \(5 + 10=3x\), so \(15 = 3x\).
Divide both sides by 3: \(x=\frac{15}{3}=5\).

Step3: Find \(m\angle P\)

Substitute \(x = 5\) into the expression for \(m\angle P\).
\(m\angle P=3x + 5=3\times5+5=15 + 5=20\).

Answer:

C. 20