Question

Solve for x. Each figure is a trapezoid.

V
T
1000
9.
Angle VTU=15+10x
Angle TVW=15+5x
U
W
10.
R
P
PS=17
QR=5+2x
Q
S


help me guys pls

Answer 1

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.