Question

in the diagram below, ad bisects ∠cab, m∠adb = 98° and m∠b = 45°. find m∠cab. step 1 m∠adb = 98° given step 2 m∠b = 45° given try m∠ cab = ° sum of angles in a triangle you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale

Explanation:

Step1: Find $\angle BAD$

In $\triangle ABD$, by the angle - sum property of a triangle ($\angle A+\angle B+\angle D = 180^{\circ}$), we have $\angle BAD=180^{\circ}-\angle ADB - \angle B$. Substituting $\angle ADB = 98^{\circ}$ and $\angle B = 45^{\circ}$, we get $\angle BAD=180^{\circ}-98^{\circ}-45^{\circ}=37^{\circ}$.

Step2: Find $\angle CAB$

Since $AD$ bisects $\angle CAB$, then $\angle CAB = 2\angle BAD$. So $\angle CAB=2\times37^{\circ}=74^{\circ}$.

Answer:

$74$