Question

1. parallelograms abcd and jklm are congruent. if ( mangle a = 2x^{circ} ) and ( mangle b = 2x - 120^{circ} ), what is ( mangle l )?

a ( 38^{circ} )
b ( 75^{circ} )
c ( 150^{circ} )
d ( 180^{circ} )

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, adjacent angles are supplementary. So, \(m\angle A + m\angle B=180^{\circ}\).
Substitute \(m\angle A = 2x^{\circ}\) and \(m\angle B=(2x - 120)^{\circ}\) into the equation:
\(2x+(2x - 120)=180\)

Step2: Solve the equation for \(x\)

Combine like - terms: \(2x+2x-120 = 180\), which simplifies to \(4x-120 = 180\).
Add \(120\) to both sides: \(4x=180 + 120\), so \(4x=300\).
Divide both sides by \(4\): \(x=\frac{300}{4}=75\).

Step3: Find \(m\angle A\)

Substitute \(x = 75\) into \(m\angle A=2x^{\circ}\), then \(m\angle A=2\times75^{\circ}=150^{\circ}\).

Step4: Use the congruence property

Since parallelograms \(ABCD\) and \(JKLM\) are congruent, \(\angle A\cong\angle J\) and \(\angle B\cong\angle K\), \(\angle C\cong\angle L\), \(\angle D\cong\angle M\). Also, in parallelogram \(ABCD\), \(\angle A\cong\angle C\) (opposite angles of a parallelogram are congruent).

So \(m\angle L=m\angle C=m\angle A = 150^{\circ}\)

Answer:

C. \(150^{\circ}\)