Question

In quadrilateral ABCD, \angle A=5x+20,\angle B=3x-30,\angle C=2x+10,and\angle D=8x.∠A=5x+20,∠B=3x−30,∠C=2x+10,and∠D=8x. Find the value of Angle B.

Equation:
x=
angle b=

Answer 1

Equation: (5x + 20) + (3x - 30) + (2x + 10) + 8x = 360

x = 20

Angle B = 30°

Explanation:

Given:

<A = 5x + 20

<B = 3x - 30

<C = 2x + 10

<D = 8x

Sum of interior angles of a quadrilateral = 360°

Therefore:

<A + <B + <C + <D = 360°

(5x + 20) + (3x - 30) + (2x + 10) + 8x = 360

Solve for x

5x + 20 + 3x - 30 + 2x + 10 + 8x = 360

Collect like terms

5x + 3x + 2x + 8x + 20 - 30 + 10 = 360

18x = 360

Divide both sides by 18

x = 360/18

x = 20

<B = 3x - 30

Plug in the value of x

<B = 3(20) - 30 = 60 - 30

<B = 30°