Answer:
To find the values of a and b such that WX←→− is perpendicular to YZ←→, we need to use the properties of perpendicular lines and angles.
First, let's recall that when two lines are perpendicular, the angles formed at their intersection are right angles (90 degrees).
Given that m∠WVY = (4a + 58)° and m∠XVY = (2b - 18)°, we can set up an equation to find the values of a and b.
Since WX←→− and YZ←→ intersect at point V, the angles ∠WVY and ∠XVY are adjacent angles. Adjacent angles are angles that share a common side and a common vertex, but have no interior points in common.
Since we want WX←→− to be perpendicular to YZ←→, the sum of ∠WVY and ∠XVY must be equal to 90 degrees.
Setting up the equation:
(4a + 58)° + (2b - 18)° = 90°
Simplifying the equation:
4a + 58 + 2b - 18 = 90
Combining like terms:
4a + 2b + 40 = 90
Subtracting 40 from both sides:
4a + 2b = 50
Now we have a linear equation with two variables, a and b. We need another equation to solve for the values of a and b.
Unfortunately, without additional information or equations, we cannot determine the exact values of a and b. We need more information to find a unique solution.