Question

find the $mangle ule$ in the triangle below.

Explanation:

Step1: Use the exterior - angle property

The exterior - angle property of a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, $\angle RUL = 109^{\circ}$ (exterior angle), and $\angle UEL=42^{\circ}$ (one non - adjacent interior angle). Let $\angle ULE = x$. Then $109^{\circ}=x + 42^{\circ}$.

Step2: Solve for \(x\)

Subtract \(42^{\circ}\) from both sides of the equation \(109^{\circ}=x + 42^{\circ}\). So, \(x=109^{\circ}-42^{\circ}\).

$$x = 67^{\circ}$$

Answer:

\(67^{\circ}\)