Question

Angle XYZ and WYU are vertical angles.

Angle XYZ = 31. Angle WYU = 7x - 4.
Find the value of x.

Options:
A) x = 5
B) x = 6
C) x = 7
D) x = 8

Answer 1

To solve for x, set the measures of the vertical angles equal, simplify the equation, and solve for x. The calculation leads to x = 5, which is option A.

Step-by-step explanation:

The student's question involves finding the value of x when given that angle XYZ and angle WYU are vertical angles, and they have provided equations for these angles: angle XYZ = 31 and angle WYU = 7x - 4. Since vertical angles are equal in measure, we can set the equations equal to each other to solve for x

1. Set the measures of the angles equal to each other because they are vertical angles: 31 = 7x - 4.
2. Add 4 to both sides to isolate terms with x on one side: 31 + 4 = 7x, which simplifies to 35 = 7x.
3. Divide both sides by 7 to solve for x: 35 / 7 = x, which simplifies to x = 5.

Therefore, the value of x is 5, which corresponds to option A).