Question

Chords AC and DB intersect at point E. Select all pairs of angles that must be congruent.

Answer 1

∠ADE and ∠ACB, ∠DEA and ∠CEB, ∠CAD and ∠CBD are pairs of angles that must be congruent.

What are congruent angles?

Congruent angles are said to be angles that have equal measure.

From the figure, we can see that;

∠ADE and ∠ACB are congruent because they are corresponding angles, corresponding angles are equal.

∠DEA and ∠CEB are congruent because they are corresponding angles

∠CAD and ∠CBD are also congruent because they are corresponding angles

Therefore, ∠ADE and ∠ACB, ∠DEA and ∠CEB,  ∠CAD and ∠CBD are pairs of angles that must be congruent.

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