line yw bisects on angle xyz if angle xyw=10x-8 and angle wyz=3x+69 x equals to???

xyw = wyz,

10x - 8 = 3x + 69
10x - 3x = 69 + 8,
7x = 77,
x = 11.

To find the value of x, we can set up an equation based on the fact that line yw bisects angle xyz.

By definition, when a line bisects an angle, it divides it into two equal angles.

From the given information, we have:
Angle xyw = 10x - 8
Angle wyz = 3x + 69

Since line yw bisects angle xyz, we can set up the following equation:
10x - 8 = 3x + 69

To solve this equation for x, we can follow these steps:

1. Simplify the equation by combining like terms:
10x - 3x = 69 + 8
7x = 77

2. Divide both sides of the equation by 7 to isolate x:
7x/7 = 77/7
x = 11

Therefore, x = 11 is the value that makes angle xyw and angle wyz equal, and line yw bisects angle xyz.