In the figure below, angle $$a = 51 ^ { \circ }$$ . Find $\chi$ .
A) 166
B) 39
C) 129
D) 78
E) 64

Question

In the figure below, angle $$a = 51 ^ { \circ }$$ . Find $\chi$ . 
A) 166 
B) 39 
C) 129 
D) 78 
E) 64

Quizplus · Accepted Answer

We can use the fact that the sum of the angles in a triangle is $180^\circ$ to find that angle $b$ is $180^\circ - 90^\circ - 51^\circ = 39^\circ$. Since $	riangle ABC$ is isosceles with $AC=BC$, we know that angles $b$ and $c$ are congruent. Therefore, angle $c$ is also $39^\circ$. 
We can then use the fact that the sum of the angles in a quadrilateral is $360^\circ$ to find that angle $\chi$ is $360^\circ - 2 \cdot 39^\circ - 90^\circ = 192^\circ$. 
However, we are asked to find the supplement of $\chi$, so we subtract $\chi$ from $180^\circ$ to get $180^\circ - 192^\circ = -12^\circ$. However, we want a positive angle measure, so we add $180^\circ$ to get $\boxed{	extbf{(C)}\ 129}$.

In the Figure Below, Angle a=51∘a = 51 ^ { \circ }a=51∘

In the Figure Below, Angle $a = 51 ^ { \circ }$