Question

1. what is the measure of angle abe?

Explanation:

Step1: Identify linear pair

Angles $\angle ABE$ and $\angle ABC$ (with $\angle DBC = 50^\circ$, so $\angle ABC = 50^\circ$) form a linear pair.

Step2: Use linear pair property

Linear pair angles sum to $180^\circ$. So $\angle ABE + \angle ABC = 180^\circ$.

Step3: Calculate $\angle ABE$

Substitute $\angle ABC = 50^\circ$: $\angle ABE = 180^\circ - 50^\circ = 130^\circ$.

Answer:

$130^\circ$