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:
[tex]\begin{gathered} \frac{3x}{3}=\frac{3}{3} \\ \\ x=1 \end{gathered}[/tex]
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°
