Question

in the diagram below, ( mangle cad = 46^{circ} ), ( mangle b = 43^{circ} ) and ( mangle adb = 107^{circ} ). find ( mangle cab ).

Explanation:

Step1: Find $\angle BAD$

In $\triangle ABD$, use the angle - sum property of a triangle ($\angle A+\angle B+\angle ADB = 180^{\circ}$). Let $\angle BAD=x$. Then $x + 43^{\circ}+107^{\circ}=180^{\circ}$.

$$x=180^{\circ}-(43^{\circ} + 107^{\circ})=180^{\circ}-150^{\circ}=30^{\circ}$$

Step2: Find $\angle CAB$

Since $\angle CAB=\angle CAD+\angle BAD$, and $\angle CAD = 46^{\circ}$, $\angle BAD = 30^{\circ}$.

$$\angle CAB=46^{\circ}+30^{\circ}$$

Answer:

$76$