Question

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

Answer 1

7 sided figure.

The 7 exterior angles add to 360; each is 180 - interior angle

7 * 180 - sum(interior angles) = 360

sum(interior angles) = 7 * 180 - 360 = 5 * 180 = 900

That's the end of the geometry part.

A+B+C+D+E+F+G=900

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

36x + 504 = 900

36x = 396

x = 11

A = 9x - 2 = 9(11)-2 = 97

Answer: 97 degrees

Answer 2

Use (n - 2) * 180 to find the sum of the measures of the interior angles of the polygon, where n is the number of sides. Plug in 7 for n.

(7 - 2) * 180 = 900

Now make all the angles in the polygon add up to 900 in an equation.

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

Combine like terms.

36x + 504 = 900

Subtract 504 from both sides.

36x = 396

Divide both sides by 36.

x = 11

Plug in 11 for x into m∠A.

A = 9x - 2 ⇒ 9(11) - 2 = 97

m∠A = 97°