Question

in the diagram below, m∠cad = 47°, m∠cab = 77° and m∠adb = 105°. find m∠b.
step angle reason
1 m∠cad = 47° given
2 m∠cab = 77° given
3 m∠adb = 105° given
m∠ = ° select a reason

Explanation:

Step1: Find $\angle BAD$

$\angle BAD=\angle CAB-\angle CAD$. Given $\angle CAD = 47^{\circ}$ and $\angle CAB=77^{\circ}$, so $\angle BAD = 77^{\circ}- 47^{\circ}=30^{\circ}$.

Step2: Use angle - sum property of a triangle

In $\triangle ABD$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle B=x$, $\angle BAD = 30^{\circ}$ and $\angle ADB=105^{\circ}$. Then $x+30^{\circ}+105^{\circ}=180^{\circ}$.

Step3: Solve for $\angle B$

$x=180^{\circ}-(30^{\circ} + 105^{\circ})=45^{\circ}$.

Answer:

$45^{\circ}$