Question

I need help and it due tomorrow!!! ill give aomethe brainlest answer​

Answer 1

Answer:

The measure of the indicated angle is 142°

Step-by-step explanation:

The sum of the measures of the interior angles of a polygon is

∑m = (n - 2) × 180°, where

• n is the number of its side or its angles

In the given figure

∵ The polygon has 6 angles

∴ n = 6

→ Use the rule above to find the sum of the measures of its interior ∠s

∵ ∑m = (6 -2) × 180°

∴ ∑m = 4 × 180°

∴ ∑m = 720°

∵ The measures of its interior ∠s are (2x - 50)°, (x + 40), 80°, (x + 20)°,

   x°, 150°

→ Add them to find their sum

∴ ∑m = 2x - 50 + x + 40 + 80 + x + 20 + x + 150

→ Add the like terms in the right side

∴ ∑m = (2x + x + x + x) + (-50 + 40 + 80 + 20 + 150)

∴ ∑m = 5x + 240

→ Equate the right sides of ∑m

∵ 5x + 240 = 720

→ Subtract 240 from both sides

∴ 5x + 240 - 240 = 720 - 240

∴ 5x = 480

→ Divide both sides by 5

∴ x = 96

→ To find the indicated angle substitute x in its measure by 96

∵ The measure of the indicated angle = 2(96) - 50

∴ The measure of the indicated angle = 192 - 50

∴ The measure of the indicated angle = 142°