Question

1. (02.04 mc)

isosceles triangle abc contains angle bisectors, ad, and that intersect at x.
if and m∠bca = 44°, what is m∠cxa? (2 points)
136°
132°
66°
44°

Explanation:

Step1: Find base angles of △ABC

Since $\overline{BA} \cong \overline{BC}$, $\triangle ABC$ is isosceles with $\angle BAC = \angle BCA = 44^\circ$.

Step2: Calculate bisected angles

$AX$ bisects $\angle BAC$, so $m\angle XAC = \frac{44^\circ}{2} = 22^\circ$.
$CX$ bisects $\angle BCA$, so $m\angle XCA = \frac{44^\circ}{2} = 22^\circ$.

Step3: Find $m\angle CXA$ via triangle sum

In $\triangle CXA$, the sum of angles is $180^\circ$.
$m\angle CXA = 180^\circ - m\angle XAC - m\angle XCA$
$m\angle CXA = 180^\circ - 22^\circ - 22^\circ$

Answer:

136°