In the figure above, what is the value of x ?

Options

A. 45
B. 90
C. 100
D. 105

Answer

D

Explanation

The figure is a quadrilateral, so the sum of the measures of its interior angles is `360^@`. The value of x can be found by using the equation 45 + 3x = 360. Subtracting 45 from both sides of the equation results in 3x = 315, and dividing both sides of the resulting equation by 3 yields x = 105. Therefore, the value of x in the figure is 105. Choice A is incorrect. If the value of x were 45, the sum of the measures of the angles in the figure would be 45 + 3(45), or `180^@`, but the sum of the measures of the angles in a quadrilateral is `360^@`. Choice B is incorrect. If the value of x were 90, the sum of the measures of the angles in the figure would be 45 + 3(90), or `315^@`, but the sum of the measures of the angles in a quadrilateral is `360^@`. Choice C is incorrect. If the value of x were 100, the sum of the measures of the angles in the figure would be 45 + 3(100), or `345^@`, but the sum of the measures of the angles in a quadrilateral is `360^@`.