Find the value of x. The diagram is not drawn to scale.

Question

A quadrilateral is shown with its bottom side extended outside the shape to the left.· The exterior angle formed at the bottom left of the quadrilateral is labeled 116 degree sign.
· The bottom left angle of the quadrilateral adjacent to the exterior angle is labeled y degree-sign.
· The top left angle of the quadrilateral is labeled x degree-sign.
· The top right angle of the quadrilateral is labeled 125 degree-sign.
· The bottom right angle of the quadrilateral is labeled 72 degree-sign.
(1 point)
Responses

x = 64o
x = 64 o

x = 86o
x = 86 o

x = 99o
x = 99 o

x = 113o
x = 113 o

Answer 1

To find the value of x, we can use the property that the sum of the interior angles of a quadrilateral is always 360 degrees.

The sum of the top left and top right angles is x + 125 degrees.

The sum of the bottom left and bottom right angles is y + 72 degrees.

So, we have the equation:

x + 125 + y + 72 = 360

Simplifying, we get:

x + y + 197 = 360

Subtracting 197 from both sides, we have:

x + y = 163

We know that the exterior angle is equal to the sum of the two remote interior angles. So, we have:

116 = x + y

Simplifying, we get:

x + y = 116

Now we have a system of equations:

x + y = 116
x + y = 163

Subtracting the first equation from the second equation, we have:

163 - 116 = x + y - (x + y)
47 = 0

This is not a true statement, which means there is no solution for x and y that satisfies both equations.

Therefore, there is no value of x that satisfies the given conditions. The correct answer is: No solution.