Question

First, determine the value of x. Then find the measure of ∠BCA. Will brainlist first correct answer.
X=_________

Answer 1

Answer:

x = 16°    ||   ∠BCA = 57°

explanation:

All the angles lie on a straight line.

A triangles total interior angle is 180°

So we need to find the inner angle of each side and they are:

• ∠ABC = 180 - ( 5x + 12 )
• ∠BCA = 180 - ( 10x - 37 )
• ∠CAB = 180 - ( 9x + 1 )

So with this:

180 - ( 5x + 12 ) + 180 - ( 10x - 37 ) + 180 - ( 9x + 1 ) = 180

180 - 5x - 12 + 180 -10x +37 + 180 -9x-9 = 180

564 - 24x = 180

-24x = 180 - 564

-24x = -384

x = 16°

Then ∠BCA = 180 - ( 10x - 37 )

                   =  180 - ( 10 * 16 - 37)

                    = 57°