SOLUTION: Given triangle ABC, point E is along side AC and point D is along side BC. Line BE and AD are the angle bisectors of angle B and A respectively. If the angle BEC = 75° and

Algebra ->  Triangles -> SOLUTION: Given triangle ABC, point E is along side AC and point D is along side BC. Line BE and AD are the angle bisectors of angle B and A respectively. If the angle BEC = 75° and       Log On


   

Question 1182638: Given triangle ABC, point E is along side AC and point
D is along side BC. Line BE and AD are the angle
bisectors of angle B and A respectively. If the angle BEC
= 75° and angle ADC = 84°, find the ACB.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let angle ABC be 2x degrees
Let angle BAC be 2y degrees

Then the angle we are to find, ACB, is (180-(2x+2y)) degrees.

Angles EBA and EBC are each x degrees; angles DAB and DAC are each y degrees.

Angle BEC is 75 degrees, so angle BEA is 180-75=105 degrees; angle ADC is 84 degrees, so angle ADB is 180-84=96 degrees.

In triangle ABD,

96+2x+y=180 [1]

In triangle ABE,

105+x+2y=180 [2]

Solve the pair of equations [1] and [2] to find x and y; then use those to find the answer to the problem.