Question

in the figure below, point B is on line segment DC. If AB = BC, what is the measure of angle ABE? FREE BRAINlIEST FOR THE FIRST PERSON TO ANSWER! Very desperate!

Answer 1

Answer:

  (A)  20°

Step-by-step explanation:

The relations between angles in a triangle and along a line can be used to find the measure of angle ABE.

Triangle angles

The congruence AB = BC tells you that ΔABC is isosceles, and that ∠C = ∠A = 30°. The sum of angles in a triangle is 180°, so the measure of angle ABC is ...

  ∠ABC = 180° -30° -30° = 120°

Angles on a line

The sum of angles along a line is 180°, so we have ...

  ∠DBE +∠EBA +∠ABC = 180°

  4x +2x +120° = 180°

  6x = 60° . . . . . . . . . . subtract 120°, collect terms

  2x = 20° . . . . . . . divide by 3

The measure of angle ABE is 20°.

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The figure is drawn to scale in the attachment.

Answer 2

just a quick addition to the superb posting by sqdancefan

Check the picture below.