∠ 1 , ∠ 2 , and ∠ 3 form a straight line. If m ∠ 3 is six more than twice m ∠ 1 , and m ∠ 2 is 27 less than m ∠ 3 , find m ∠ 2 .

Question

, , and  form a straight line. If  is six more than twice , and  is  less than , find .

Answer 1

1+2+3 = 180 degrees = a straight line, call them A, B and C

C = 6+2A

2A = C-6

A = C/2 -3

A = (B+27)/2 - 3

B = C-27

C=B+27

Find B (angle 2)

A+B+C = 180

(B+27)/2 - 3 + B + B+27 = 180

B/2 + 27/2 - 3 + 2B +27 = 180

5B/2 = 180 - 27- 27/2 + 3

B = (2/5)(360/2 - 81/2 + 6/2) = (2/5)(285/2) = 285/5 = 57 degrees = angle 2

C=B+27 = 84 degrees = angle 3

A = (B+27)/2 -3= (57+27)/2 -3= 84/2-3 = 42-3 = 39 degrees= angle 1