Given:
VYX = 23x - 5
WYX = 18x - 2
VYW = 3x + 7
Find all three angles.
To find the angles in the given scenario, we need to use the properties of angles formed by intersecting lines.
1. Start by drawing a diagram to represent the given information. Label the three angles as VYX, WYX, and VYW, as given in the problem.
2. By applying the Angle Sum Property of triangles, we know that the sum of the angles in a triangle is always 180 degrees.
3. Begin by setting up an equation for the sum of the angles in triangle VYX: VYX + WYX + VYW = 180 degrees.
4. Substitute the given expressions for the angles into the equation:
(23x - 5) + (18x - 2) + (3x + 7) = 180 degrees.
5. Simplify the equation by combining like terms: 23x + 18x + 3x - 5 - 2 + 7 = 180 degrees.
44x + 0 = 180 degrees.
6. Solve the equation for x: 44x = 180 degrees.
x = 180 degrees / 44 = 4.09 degrees (approximate value).
7. Now that we have the value of x, we can substitute it back into each expression to find the measures of the angles.
Angle VYX = 23x - 5 = 23(4.09) - 5 = 93.07 degrees (approximate value).
Angle WYX = 18x - 2 = 18(4.09) - 2 = 72.62 degrees (approximate value).
Angle VYW = 3x + 7 = 3(4.09) + 7 = 19.27 degrees (approximate value).
So, the three angles are approximately:
VYX ≈ 93.07 degrees,
WYX ≈ 72.62 degrees, and
VYW ≈ 19.27 degrees.