SOLUTION: Hello! I don't understand these two questions, if its possible, please help me solve this step by step asap, thank you sooo much, the link leads to the two questions https://docs.

Algebra ->  Triangles -> SOLUTION: Hello! I don't understand these two questions, if its possible, please help me solve this step by step asap, thank you sooo much, the link leads to the two questions https://docs.      Log On


   

Question 1108275: Hello! I don't understand these two questions, if its possible, please help me solve this step by step asap, thank you sooo much, the link leads to the two questions
https://docs.google.com/document/d/1zdOAakUWB1eDjC3CwSlpk4Dp1TcYa56U6dOMImDdGwc/edit?usp=sharing
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
first diagram:

angle AEB = DEC because vertical angles are equal.

side AE = side EC because line segment AEC bisected by line segment BED.

side BE =side ED because line segment BED bisected by line segment AEC.

triangles ABE congruent to triangle CDE by SAS postulate.

side AE congruent to side EC
side BE congruent to side ED
angle AEB congruent to angle CED

two triangle are congruent if the corresponding sides and the included angle between them are congruent.

your solution is triangle ABE congruent to triangle CDE by SAS.

second diagram:

the sum of the remote interior angles is equal to the exterior angle.

this means that angle A + angle B = angle BCD.

you should get:

5x-135 + 5x-155 = 6x - 122.

combine like terms to get 10x - 290 = 6x - 122

subtract 6x from both sides of this equation and add 290 to both sides of this equation to get 10x - 6x = 290 - 122.

combine like terms to get 4x = 168

divide both sides of this equation by 4 to get x = 42

when x = 42, you get:

angle B = 5x - 135 = 75
angle A = 5x - 155 = 55
angle BCD = 6x - 22 = 130

angle BCA is supplemental to angle BCD, therefore angle BCA is equal to 180 - 130 = 50

you get:

angle B = 75
angle A = 55
angle C = 50

angle C is the same as angle BCA.

sum of the angles of a triangle is equal to 180.
75 + 55 + 50 = 180
this part checks out.

sum of the remote interior angles is equal to the exterior angle.
angle A plus angle B = 130
angle BCD = 130
this part checks out.

your solution is that angle BCA is equal to 50 degrees.