Answer:
<A = 124
Step-by-step explanation:
Remark
This figure has 7 angles. Therefore it can have 5 lines drawn from 1 vertex to all the other vertexes. That gives you 5 triangles. See the diagram below to see the result of what I have just described. The sum total of all the interior angles is 5 * 180 = 900
Equation
Add the seven given angles from your figure to equal 900
(9x - 2) + (10x + 2) + 165 + 100 + (5x + 83) + (12x + 18) + 138 = 900
Solution
Now add all the like terms on the left together.
- Terms Containing "x"s: 9x + 10x + 5x +12x = 36x
- Terms not containing "x"s: -2 + 2 + 165 + 100 + 83 + 18+ 138 = 504
So this simplifies to
36x + 504 = 900 Subtract 504 from both sides
36x + 504 - 504 = 900 - 503 Do the subtraction
36x = 396 Divide by 36 on both sides
x = 396/36 Do the division
x = 14
Answer
But you want angle A.
<A = 9x - 2 = 9*14 - 2 = 126 - 2 = 124
