Question

quadrilateral qrst is an isosceles trapezoid and (mangle r = 4u - 84^{circ}). what is the value of (u)?

Explanation:

Step1: Recall property of isosceles trapezoid

In an isosceles trapezoid, base - angles are equal. So, $\angle R=\angle S$.

Step2: Set up the equation

We know that $m\angle R = 4u-84^{\circ}$ and $m\angle S = 136^{\circ}$. So, $4u - 84=136$.

Step3: Solve the equation for u

Add 84 to both sides of the equation: $4u=136 + 84$.
$4u=220$.
Divide both sides by 4: $u=\frac{220}{4}=55$.

Answer:

$55$