Question

Consider parallelogram JKLM below.

Use the information given in the figure to find mLNJK, x, and mLNKJ.
K
N
4x - 3
13
AL
50°
42°
M

Answer 1

• ∠NJK = 50°
• x = 4
• ∠NKJ = 42°

Explanation:

You want a couple of interior angles and the value of x given the parallelogram in the figure.

Angles

The diagonals of a parallelogram bisect each other, and divide the figure into two pairs of congruent triangles. Here, the congruent triangles of interest are ...

∆NKJ≅∆NML

In these triangles, that means ...

∠J ≅ ∠L = 50° = ∠NJK

∠K ≅ ∠M = 42° = ∠NKJ

Segments

The halves of diagonal JL are congruent, so we have ...

4x -3 = 13

4x = 16 . . . . . . . . add 3

x = 4 . . . . . . . . . divide by 4