Question

using the image provided, find m∠uoa. 83° 42° 47° 97°

Explanation:

Step1: Recall exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In $\triangle EOU$, $\angle AEU$ is an exterior angle.

Step2: Set up the equation

We know that $\angle AEU = 63^{\circ}$, and the two non - adjacent interior angles of $\triangle EOU$ are $\angle U = 21^{\circ}$ and $\angle UOA=x$. So, $\angle AEU=\angle U+\angle UOA$.

Step3: Solve for $\angle UOA$

Substitute the known values into the equation: $63^{\circ}=21^{\circ}+x$. Then, $x = 63^{\circ}-21^{\circ}=42^{\circ}$. So, $m\angle UOA = 42^{\circ}$.

Answer:

B. $42^{\circ}$