Question

In the diagram below, line AB and line CD intersect at point P. Name the angle that is always congruent to <APC​

Answer 1

<dpb because they’re vertical angles (they’re directly across from each other)

Answer 2

Answer:  The required angle that is always congruent to angle APC is angle BPD.

Step-by-step explanation:  Given that in the diagram shown, the lines AB and CD intersect each other at the point P.

We are to name the angle that is always congruent to angle APC.

​ We know that

when two straight line intersect each other, we get two pairs of vertically opposite angles.

The two angles in each pair of vertically opposite angles are congruent to each other.

So, here the lines AB and CD are intersecting at the point P and the two pairs of vertically opposite angles are

(∠APC and ∠BPD)  and  (∠BPC and ∠APD).

Therefore, we get

∠APC ≅ ∠BPD  and  ∠BPC ≅ ∠APD.

Thus, the required angle that is always congruent to angle APC is angle BPD.