Answer:
10
Explanation:
To solve for x in a trapezoid where Angle VTU is equal to 15+10x and Angle TVW is equal to 15+5x, we can use the fact that the sum of the interior angles of a trapezoid is equal to 360 degrees.
In a trapezoid, the two base angles (the angles formed by the bases and one of the legs) are congruent. Therefore, we can set up an equation using the given angles:
Angle VTU + Angle TVW + Angle VWT + Angle UTW = 360
Substituting the given values:
(15+10x) + (15+5x) + Angle VWT + Angle UTW = 360
Simplifying the equation:
30 + 15x + Angle VWT + Angle UTW = 360
Now, we need to find the values of Angle VWT and Angle UTW. In a trapezoid, the non-base angles (the angles formed by the legs and one of the bases) are supplementary. Therefore, we can set up another equation:
Angle VWT + Angle UTW = 180
Substituting this equation into the previous equation:
30 + 15x + (Angle VWT + Angle UTW) = 360
30 + 15x + 180 = 360
Combining like terms:
15x + 210 = 360
Subtracting 210 from both sides:
15x = 150
Dividing both sides by 15:
x = 10
Therefore, the value of x in the given trapezoid is 10.