Question

in the diagram below, $overline{ad}perpoverline{dc}$, $mangle c = 55^{circ}$ and $mangle b = 44^{circ}$. find $mangle cab$. step angle reason 1 $mangle c = 55^{circ}$ given 2 $mangle b = 44^{circ}$ given try $manglesquare=square^{circ}$ select a reason

Explanation:

Step1: Find $\angle CAD$ in right - triangle $ADC$

In right - triangle $ADC$ with $\angle D = 90^{\circ}$ and $\angle C=55^{\circ}$, using the angle - sum property of a triangle ($\angle A+\angle B+\angle C = 180^{\circ}$). So, $\angle CAD=180^{\circ}-\angle D-\angle C=180^{\circ}-90^{\circ}-55^{\circ}=35^{\circ}$.

Step2: Find $\angle CAB$ in triangle $ABC$

In triangle $ABC$, we know $\angle B = 44^{\circ}$. Let $\angle CAB=x$. Using the angle - sum property of a triangle ($\angle CAB+\angle B+\angle ACB = 180^{\circ}$). First, we found $\angle CAD = 35^{\circ}$.
We know that in triangle $ABC$, $\angle CAB=180^{\circ}-\angle B-\angle C$. Since $\angle C = 55^{\circ}$ and $\angle B = 44^{\circ}$, then $\angle CAB=180^{\circ}-44^{\circ}-55^{\circ}=81^{\circ}$.

Answer:

$81^{\circ}$