A trapezium with two opposite angles is labeled as 101 degrees. The third angle is bisected with a diagonal line making the angles 11 x degrees, and left parenthesis 9 x plus 6 right parenthesis degrees.
The quadrilateral shown is a
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x =
The quadrilateral shown is an isosceles trapezium.
To find the value of x, we can use the fact that the angles in a trapezium add up to 360 degrees.
The two opposite angles are labeled as 101 degrees each, so their sum is 101 + 101 = 202 degrees.
The third angle is bisected by the diagonal line, so we can consider the two resulting angles as a pair. We can represent the third angle as 2x.
The sum of the three angles in the trapezium is 202 + (11x) + (9x + 6) = 360.
Combining like terms, we get 20x + 208 = 360.
Subtracting 208 from both sides, we have 20x = 152.
Dividing both sides by 20, we find x = 7.6.