The value of the angle m∠ ZLK is 75° and m∠MLZ as 55°.
Given, m∠ZLK = x + 86°
m ∠MLZ = 130°
and m∠MLZ = x+66
we know that ∠ZLK + ∠MLZ = ∠MLK
therefore, substitute the values:
⇒ (x+86)+(x+66) = 130
⇒ x + 86 + x + 66 = 130
⇒ arrange the like terms.
⇒ 2x + 152 = 130
⇒ 2x = 130 - 152
⇒ 2x = -22
⇒ x = -22/2
⇒ x = -11
now substitute the x value to get m∠ZLK
now m∠ZLK = x+86
m∠ZLk = -11+86
m∠ZLK = 75°
and m∠MLZ = x+66
m∠MLZ = -11+66
m∠MLZ = 55°
Hence we get the values of the angle m∠ ZLK as 75°.
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