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!
2 answers:
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.
<h3>Triangle angles</h3>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°
<h3>Angles on a line</h3>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°.
__
The figure is drawn to scale in the attachment.
You might be interested in
Using the Fundamental Counting Theorem, it is found that there are 10 positive three-digit integers have the hundreds digit equal to 7 and the units (ones) digit equal to 1.
<h3>What is the Fundamental Counting Theorem?</h3>It is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
The number of options for each selection are given as follows, considering there are 10 possible digits, and that the last two are fixed at 7 and 1, respectively:
Hence, the number of integers is given by:
N = 10 x 1 x 1 = 10.
More can be learned about the Fundamental Counting Theorem at brainly.com/question/24314866
#SPJ1