Question

11. If mNJ = "

170", mMK = (5x + 8), and mZMLK = (4x + 3)", find mZMLK.
,
M
o
K

Answer 1

∠ MLK = 51°

Explanation:

the secant- secant angle MLK is half the difference of the measures of the intercepted arcs , that is

∠ MLK =
`(1)/(2)` ( NJ - MK ) ← substitute values

4x + 3 =
`(1)/(2)` (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°