x is the opposite angle to one of the interior angles in the quadrilateral. The interior angles to the quadrilateral are. 1. For the pentagon 180-108 = 72 degrees 2. For the hexagon 180-120 = 60 degrees 3. For the angle with both hexagon and pentagon = 360 - 180 - 120 = 132 4. For the opposite angle to x, since it's the last of the 4 angles in the quadrilateral will be 360 - 72 - 60 - 132 = 96 degrees
And since x is opposite this 4th angle, it too will have the value 96 degrees.
<span>96 degrees
Looking at the diagram, you have a regular pentagon on top and a regular hexagon on the bottom. Towards the right of those figures, a side is extended to create an irregularly shaped quadrilateral. And you want to fine the value of the congruent angle to the furthermost interior angle. So let's start.
Each interior angle of the pentagon has a value of 108. The supplementary angle will be 180 - 108 = 72. So one of the interior angles of the quadrilateral will be 72.
From the hexagon, each interior angle is 120 degrees. So the supplementary angle will be 180-120 = 60 degrees. That's another interior angle of the quadrilateral.
The 3rd interior angle of the quadrilateral will be 360-108-120 = 132 degrees. So we now have 3 of the interior angles which are 72, 60, and 132. Since all the interior angles will add up to 360, the 4th angle will be 360 - 72 - 60 - 132 = 96 degrees.
And since x is the opposite (or congruent) angle to this 4th interior angle, it too has the value of 96 degrees.</span>
