SOLUTION: In the triangle shown below, DB = DC, DE=CE and <DAE = 48°. Find the measure of <ACB. https://ibb.co/48VRX5b

Question 1208873: In the triangle shown below, DB = DC, DE=CE and https://ibb.co/48VRX5b
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Strategy:
(1) Use the given congruent line segments to define variables for the measures of the two pairs of congruent angles in triangles BDC and EDC
(2) Use those variables to find expressions for the measures of all the other angles in the figure (note some of these will not be used in solving the problem)
(3) BC and DE are parallel, so angles CBD and EDA are congruent. Use the expressions for the measures of those two angles to solve the problem

DB = DC, so angles DBC and DCB are congruent. Let x be the measure of each of those two angles. That makes the measure of angle BDC 180-2x.

DE = CE, so angles ECD and EDC are congruent. Let y be the measure of each of those two angles.

The sum of the measures of angles BDC, CDE, and EDA is 180 degrees, so the measure of angle EDA is 2x-y.

DE is parallel to BC, so angles CBD and EDA are congruent. So

x = 2x-y --> y = x.

In triangle ABC, the sum of the measures of the angles is 180 degrees:

x + (x+y) + 48 = 180
x + (x+x) = 132
3x = 132
x = 44

The measure of angle ACB is x+y = 2x = 88.

ANSWER: 88 degrees

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