Question

in the figure below, m∠abd = 95°, m∠cbd = 60°, and be bisects ∠cbd. find m∠abe. m∠abe = 0°

Explanation:

Step1: Find half of ∠CBD

Since BE bisects ∠CBD and ∠CBD = 60°, then ∠CBE=∠EBD = $\frac{1}{2}\times\angle CBD$.
∠CBE = $\frac{1}{2}\times60^{\circ}=30^{\circ}$.

Step2: Find ∠ABE

We know that ∠ABD = 95°, and ∠ABD=∠ABE + ∠EBD. So ∠ABE=∠ABD - ∠EBD.
∠ABE = 95° - 30° = 65°.

Answer:

65