Question

Lines CE and AD intersect at B.

What is the measure of angle DBE?
Group of answer choices

37∘

143∘

53∘

127∘

Answer 1

The measure of angle DBE is 37° ⇒ (A)

Explanation:

If two lines are intersecting at a point, then every two vertically opposite angles are equal in measure

Example:

If line XY intersects line MN at point Z, then angle MZX, angle NZY are vertically opposite angles, and angle MZY, angle NZX are vertically opposite angles

Let us use this fact to solve the question

∵ Line CE intersects line AD at point B

∴ ∠ ABC and angle ∠DBE are vertically opposite angles

∴ m∠ABC = m∠DBE

∵ m∠ABC = 37°

∴ m∠DBE = 37°

The measure of angle DBE is 37°