Question

Find the value of x. Then find the missing angle measures of the polygon.



x=

All angles labeled (x−30)∘ are what?º
help please

Answer 1

The sum of the angles equals 540

There are 3 angles that measure (x - 30) and 2 angles that measure (x)

3(x - 30) + 2(x) = 540

3x - 90 + 2x = 540

5x - 90 = 540

5x = 630

x = 126

x - 30   = 126 - 30   = 96

Answer: x = 126,  x-30 = 96

Answer 2

The sum of angles is calculated using the formula (n - 2) × 180°

Looking at the diagram, this polygon has 5 sides. Inputting this into the formula:

(5 - 2)  × 180°

3 × 180° = 540°

Part A

Solving for x

x° + x° + (x - 30)° + (x - 30)° + (x - 30)° = 540°

x° + x° + x° - 30° + x° - 30° + x°- 30° = 540°

x° + x° + x° + x° + x° - 30° - 30°  - 30° = 540°

5x° - 90° = 540°

5x° = 540° + 90°

5x° = 630°

Divide both sides by 5

5x°/5 = 630°/5

x = 126°

Therefore the value of x = 126°

Part B

Solving for this angle : (x - 30)°

x = 126°,

(126 - 30)° = 96°

Therefore, the angles labeled (x−30)° are 96º

Part C

Therefore, the measures of the missing angles of the polygon are:

126°, 126°, 96°, 96° and 96°

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