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°
