Answer:
A. 2x +17° = 3x -4°
B. x = 21°; ∠LKN = 59°
Step-by-step explanation:
Given alternate interior angles of 2x +17° and 3x -4°, you want an equation for x, and the measure of these angles.
A. Equation
The marked angles are alternate interior angles at transversal KN with respect to parallel lines KL and MN. That means they are congruent. An equation showing they have the same measure can be used to solve for x.
2x +17° = 3x -4°
B. Angle
Adding 4° -2x to both sides of the equation gives ...
21° = x
Using this value in the expression for ∠LKN, we have ...
∠LKN = 2(21°) +17° = 42° +17°
∠LKN = 59°
