Question

The sum of the angle measures of a quadrilateral is 360°. Write and solve an equation to find the value of x.

Answer 1

Given: The shape is a quadrilateral, which means four angles with a sum of 360°. The known measures are 112 and 73, and there are two unknown measures. They are probably identical, considering the fact that they both have the variable x.

Numerically, this would be $112 + 73 + x + x = 360$.

Simplify.

$(112 + 73) + (x + x)$ = 360

--> $185 + 2x = 360$

Isolate the variable by subtracting 185 from both sides.

$2x = 360 - 185$

--> 2x = 175

If 175 is twice as much as x, then $x = \frac{175}{2}$

x = $87.5$

Plug in the value of x:

$112 + 73 + 2(87.5) = 360$

--> $185 + 175 = 360$

X has an angle measure of 87.5°