Respuesta :

mathstudent55

Answer:

x = 50

Step-by-step explanation:

The sum of the measures of the interior angles of a polygon of n sides is

(n - 2)180

This polygon is a quadrilateral with 4 sides. n = 4

(n - 2)180 = (4 - 2)180 = 2(180) = 360

The sum of the measures of the interior angles of the quadrilateral is 360 degrees.

We have angles of 110 deg, 2x deg, x + 10 deg, and 90 deg. We add their measures and set teh sum equal to 360. Then we solve for x.

x + 10 + 2x + 110 + 90 = 360

3x + 210 = 360

3x = 150

x = 50

kirabowen15
First we ate gonna write an equation to solve for x

2x + x + 10 + 110 = 360

When we add everything it’s equal to 360 because there are two triangles in a quadrilateral and each triangle measures 180. So 2 times 180 is equal to 360.

Or to simply put it all the angles in a quadrilateral measures 180.

Ok so let’s solve the equation to find x

2x + x + 10 + 110 = 360
3x + 120 = 360
3x = 360 - 120
3x/3 = 240/3
x = 80