Question

Consider parallelogram JKLM below.

Use the information given in the figure to find x, m
ZL, and m ZLMK.

Answer 1

x = 5

∠L = 114°

∠ LMK = 31°

Answer 2

x = 5

∠L = 114°

∠ LMK = 31°

Explanation:

In parallelogram, opposite sides are parallel and equal.

3x = 15

Divide both sides by 3

3x/3 = 15/3

x = 5

In parallelogram, opposite angles are equal

∠L = ∠J

∠L = 114°

In ΔJKM,

∠J + ∠JKM + ∠JMK = 180 {Angle sum property of triangle}

114 + ∠JKM + 35 = 180

149 + ∠JKM =180

∠JKM = 180 - 149

∠JKM = 31°

JK & ML are parallel and KM is transversal

Therefore, ∠ LMK = ∠JKM { oppoiste interior angles are congruent}

∠ LMK = 31°