Question

FIGURE ABCD BELOW IS A QUADRILATERAL. WHAT IS THE VALUE OF X ?

A. 15
B. 40
C. 45
D. 65

Answer 1

x = 45

Explanation:

Note that:

The sum of the interior angles of a quadrilateral is 360°.

Angle: ADC+BAD+ABC+BCD = 360°

Thus, Substitute ∠ABC = 3x, ∠BAD = (2x-5) , ∠ ADC = (x+15), ∠ BCD = 80 turn into ADC+BAD+ABC+BCD = 360° :

Also known as :

(x+15) +(2x-5) + 3x+80=360

Solving for x

Add the numbers

x + 90+2x+3x=360

Combine like terms

6x + 90=360

subtract 90 from both sides

6x = 270

x = 45

Hence the value of x = 45

Kavinsky

Answer 2

C. 45

Explanation:

1) Sum of the interior angles of any shape:

(n - 2) x 180, where n is the number of vertices of a shape. In this case, we have 4 vertices.

= (4 - 2) x 180

= 2 x 180

= 360°

2) Add all the given values equating to 360.

2x - 5 + 3x + 80 + x + 15 = 360

6x + 90 = 360

6x = 360 - 90

6x = 270

x = 270/6

x = 45