Question

Given ABC = DCB; m A= 45°; m ABC = 3x;

m DBC = 30 and m ACB = 4y + 2, find the values of x and y.

Answer 1

Well, since the two triangles are congruent, angles DBC and ACB are equal to each other.
So, 30=4y + 2
Subtract 2, 28=4y
Divide by 4, 7 = y


Now since all angles in a triangle are equal to 180 you can do :
180 = (45 + 3x + 30)
Simplify, 180=3x +75
Subtract 75, 105 = 3x
Divide by 3, 35=x