Question

pqrs is an isosceles trapezoid with bases $overline{sr}$ and $overline{pq}$, $mangle p = 3x + 5$, and $mangle q = 6x - 10$. find $mangle p$. (not drawn to scale) a 160 b 17 c 20 d 5

Explanation:

Step1: Use property of isosceles trapezoid

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

Step2: Solve for \(x\)

Subtract \(3x\) from both sides:
\[5 = 6x-3x - 10\]
\[5=3x - 10\]
Add 10 to both sides:
\[3x=5 + 10\]
\[3x=15\]
Divide both sides by 3:
\[x = 5\]

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