Question

Consider parallelogram JKLM below.use the information given in the figure to find m

Answer 1

Here, we have a parallelogram JKLM.

Given:

JK = 3x

LM = 3

m∠J = 106°

m∠KMJ = 34°

A parallelogram is a quadilateral that has equal opposite angles and the opposite sides are also equal.

Thus, we have:

• m∠L = m∠J = 106°

m∠L = 106°

• x:

Here, JK is opposite side LM. SInce they are opposite sides, they have equal length.

Thus, we have:

JK = LM

3x = 3

Divide both sides by 3:

`\begin{gathered} (3x)/(3)=(3)/(3) \\ \\ x=1 \end{gathered}`

x = 1

• m∠LKM:

Apply the alternate interior angles theorem. Alternate interior angles are congruent.

∠LKM and ∠KMJ are alternate interior angles. This means they are congruent.

Thus, we have:

m∠LKM = m∠KMJ = 34°

m∠LKM = 34°

ANSWER:

• m∠L = 106°

• x = 1

• m∠LKM = 34°