SOLUTION: How do you find an exterior angle when all you know is ABC + BCA + CAB = 180 5x + 8 + 6x + 22 + 3x - 25 = 180 14x =175 x = 12.5 M<BAC = 5X+8 = 70.5 M<ABC=6X+22 = 97 M<BCA=3X-25 = 1

Algebra ->  Angles -> SOLUTION: How do you find an exterior angle when all you know is ABC + BCA + CAB = 180 5x + 8 + 6x + 22 + 3x - 25 = 180 14x =175 x = 12.5 M<BAC = 5X+8 = 70.5 M<ABC=6X+22 = 97 M<BCA=3X-25 = 1      Log On


   

Question 924549: How do you find an exterior angle when all you know is ABC + BCA + CAB = 180 5x + 8 + 6x + 22 + 3x - 25 = 180 14x =175 x = 12.5 M
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
you know is ABC+%2B+BCA+%2B+CAB+=+180
you also know it's a triangle


you know 5x+%2B+8+%2B+6x+%2B+22+%2B+3x+-+25+=+180
14x+=175
x+=+12.5
measure of each angle is:
M< BAC+=+5X%2B8+=+70.5
M< ABC=6X%2B22+=+97
M< BCA=3X-25+=+12.5
you also know that an measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles
let's exterior angles be A, B, and C (the letter of each vertex)
then
M< A=M< ABC%2BBCA=>M< 97%2B12.5=>M< 109.5
M< B=M< BAC%2BBCA=>M< 70.5%2B12.5=>M< 83
M< C=M< BAC%2BABC=>M< 70.5%2B97=>M< 167.5

or, solve it using the sum of an exterior angle and its corresponding interior angle which is 180
exterior angle A and BAC sum up to 180
so,
A=180-BAC=180-70.5=109.5
B=180-ABC=180-97=83
C=180-BCA=180-12.5=167.5