Question

for exercises 1 - 5, use the figure at right to complete each statement. 1. a is the ________ of ∠bae. 2. (overline{ad}) is the ______ of ∠bae. 3. (overline{ad}) is a ______ of ∠dae. 4. if (mangle bac = 42^{circ}), then (mangle cae=) ______. 5. ∠iab = ________.

Explanation:

Step1: Identify angle - bisector property

Since $\overrightarrow{AC}$ and $\overrightarrow{AD}$ are angle - bisectors as indicated by the equal - angle markings. $\angle BAE$ is divided into four equal angles.

Step2: Calculate $\angle CAE$

Given $m\angle BAC = 42^{\circ}$, and $\angle BAC=\angle CAE$ (because of angle - bisector properties shown in the figure). So $m\angle CAE = 42^{\circ}$.

Answer:

$42^{\circ}$