Answer:
∠ MLK = 51°
Step-by-step explanation:
the secant- secant angle MLK is half the difference of the measures of the intercepted arcs , that is
∠ MLK = [tex]\frac{1}{2}[/tex] ( NJ - MK ) ← substitute values
4x + 3 = [tex]\frac{1}{2}[/tex] (170 - (5x + 8) ) ← multiply both sides by 2 to clear the fraction
8x + 6 = 170 - 5x - 8
8x + 6 = 162 - 5x ( add 5x to both sides )
13x + 6 = 162 ( subtract 6 from both sides )
13x = 156 ( divide both sides by 13 )
x = 12
Then
∠ MLK = 4x + 3 = 4(12) + 3 = 48 + 3 = 51°
