Question

Can somebody help me? With those three problems please

Answer 1

Answer:

15. $x = 8$

16. m<V = 103°

17. $x = 14$

Step-by-step 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

$x = 14$