Question

In a quadrilateral, the given angle measures are x^∘, 125^∘, 132^∘, and 72^∘. The sum of its angles is 360^∘. Set up an equation to find the value of the missing angle. Solve the equation and express your answer in the form:

x = _____ degrees

A. x = 31^∘
B. x = 33^∘
C. x = 95^∘
D. x = 131^∘

Answer 1

The value of the missing angle x in the quadrilateral is 31 degrees as determined by setting up the equation using the sum of the angles in a quadrilateral.

Step-by-step explanation:

To find the value of the missing angle (x) in a quadrilateral, we know that the sum of the angles in any quadrilateral is 360 degrees. To set up the equation to find x, we add all the given angles and set the sum equal to 360 degrees:

x + 125 + 132 + 72 = 360

Combining the known angles:

x + 329 = 360

To solve for x, subtract 329 from both sides of the equation:

x = 360 - 329

This gives us:

x = 31 degrees

Therefore, the missing angle measure is 31 degrees, which corresponds to option A.