Question

Find the measure of angle A. Show equations and all work that leads to your answer.

Answer 1

∠A = 97°

Explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 7, hence

sum = 180° × 5 = 900°

Sum the given angles and equate to 900

10x + 2 + 165 + 100 + 5x + 83 + 12x + 18 + 138 + 9x - 2 = 900

36x + 504 = 900 ( subtract 504 from both sides )

36x = 396 ( divide both sides by 36 )

x = 11

Hence

∠A = 9x - 2 = (9 × 11) - 2 = 99 - 2 = 97°

Answer 2

Since it has 7 sides it all has to add up to 900 degrees (180 times (number of sides - 2)

900 = 138 + (12x + 18) + (5x + 83) + 100 + 165 +(10x + 2) + (9x -2)

900 = 12x + 5x + 10x + 9x + 138 + 18 + 83 + 100 + 165 + 2 - 2

900 = 36x + 504

900 - 504 = 36x

396 = 36x

x =11

so: 138 + (12*11 + 18) + (5*11 + 83) + 100 + 165 + (10*11 + 2) + (9*11-2)

138 + 150 + 138 + 100 + 165 + 112 + 97

900 degrees