Find the value of x. The diagram is not to scale. Lines f and g are parallel.
A quadrilateral is formed when two segments are drawn connecting a pair of horizontal lines. The segments are angled in opposite directions. The angle formed in the top left interior of the quadrilateral is labeled 5 x. The angle formed in the bottom left interior of the quadrilateral is labeled 9 x plus 26.
(1 point)
Responses
10
10
11
11
12
12
–11
–11
We can use the fact that the sum of the angles in a quadrilateral is 360 degrees to solve for x.
In the quadrilateral, we have two pairs of opposite angles: one pair is labeled 5x and the other pair is labeled 9x+26. The sum of the angles in the quadrilateral can be written as:
(5x) + (9x+26) + (5x) + (9x+26) = 360
Simplifying this equation, we get:
28x + 52 = 360
Subtracting 52 from both sides, we have:
28x = 308
Dividing both sides by 28, we find:
x = 11
Therefore, the value of x is 11.