Question

which two angles are supplementary? a) ∠abe and ∠dbc b) ∠abd and ∠ebc c) ∠abd and ∠dbc d) ∠abe and ∠ebd

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180 degrees. A linear - pair of angles is supplementary.

Step2: Analyze the given angles

In the figure, $\angle ABD$ and $\angle DBC$ form a linear pair since they share a common side $BD$ and their non - common sides $AB$ and $BC$ form a straight line $AC$. The measure of a straight - line angle is 180 degrees. So, $\angle ABD+\angle DBC = 180^{\circ}$.

Answer:

C. $\angle ABD$ and $\angle DBC$