Question

Can somebody help me? With those three problems please

Answer 1

15.
`x = 8`

16. m<V = 103°

17.
`x = 14`

Explanation:

15. The figure given is quadrilateral. Sum of interior angles of a quadrilateral = 360°

Therefore:

`(10x + 6) + (13x - 2) + (8x - 1) + (180 - 71) = 360`

Solve for x

`10x + 6 + 13x - 2 + 8x - 1 + 109 = 360`

Add like terms

`31x + 112 = 360`

Subtract 112 from each side

`31x = 248`

Divide both sides by 31

`x = 8`

16. The polygon is a hexagon. Sum of interior angles of a hexagon = 720. Therefore:

`90 + (7x + 3) + 128 + (5x + 8) + 111 + (9x - 19) = 720`

Solve for x

`90 + 7x + 3 + 128 + 5x + 8 + 111 + 9x - 19 = 720`

Add like terms

`321 + 21x = 720`

Subtract 321 from each side

`21x = 399`

Divide both sides by 21

`x = 19`

m<V = 5x + 8

Plug in the value of x

m<V = 5(19) + 8 = 95 + 8

m<V = 103

17. The polygon is a regular pentagon. This means each of the angles measures 108°. The sum of the interior angles all together is 540.

Therefore:

`(9x - 18) = 108`

Solve for x

`9x - 18 = 108`

Add 18 to both sides

`9x = 126`

Divide both sides by 9

`x = 14`