Find the value of x. The diagram is not drawn to scale.
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
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.
To find the value of x, we can use the fact that the sum of the interior angles of a quadrilateral is always 360 degrees.
First, let's calculate the value of y.
Since the exterior angle at the bottom left of the quadrilateral is 116 degrees, the corresponding interior angle adjacent to it is 180 degrees - 116 degrees = 64 degrees.
Now, since the sum of the angles of a quadrilateral is 360 degrees, we can write an equation:
x + y + 125 + 72 = 360
Substituting the known values, we have:
x + 64 + 125 + 72 = 360
x + 261 = 360
To solve for x, we need to isolate it on one side of the equation.
Subtracting 261 from both sides, we get:
x = 360 - 261
x = 99 degrees
Therefore, the value of x is 99 degrees.
To find the value of x, we can use the fact that the sum of the interior angles of a quadrilateral is always 360 degrees.
Since we know the measures of the other three angles (y, 125, and 72 degrees), we can find the measure of x by subtracting the sum of those angles from 360 degrees.
The sum of the other three angles is y + 125 + 72 degrees.
Therefore, we have:
360 degrees = y + 125 + 72 degrees.
To solve for y, we need to subtract 125 and 72 from both sides of the equation:
360 degrees - 125 degrees - 72 degrees = y.
This simplifies to:
163 degrees = y.
Now, we know the value of y is 163 degrees.
To find the value of x, we subtract the sum of the other three angles (163 degrees) from 360 degrees:
x = 360 degrees - 163 degrees.
This simplifies to:
x = 197 degrees.
Therefore, the value of x is 197 degrees.
So, the correct answer is:
x = 197o