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.
