Question

parallelogram properties - angles
score: 1/5 penalty: 0.25 off
question
in parallelogram lmnp if ( mangle lmn = 120^{circ} ) find ( mangle npl ).

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, adjacent angles are supplementary. So, \(m\angle LMN + m\angle MNP= 180^{\circ}\). But also, in parallelogram \(LMNP\), \(m\angle NPL=\frac{1}{2}(180 - m\angle LMN)\) (because in a parallelogram, the angle bisector property can be used. Another way: since \(LMNP\) is a parallelogram, \(LM\parallel NP\). Let's consider triangle formed if we bisect some angles (alternatively, using the property that consecutive angles are supplementary and if we assume the angle \(x\) is half - of the supplementary angle of \(\angle LMN\) in a non - complex parallelogram angle - related problem setup as per basic parallelogram angle rules taught in geometry basics).

Step2: Calculate the value of \(x\)

Given \(m\angle LMN = 120^{\circ}\). Then \(x=\frac{180 - 120}{2}\).

$$x=\frac{60}{2}=60$$

Answer:

$60$