Question

analyze the diagram below and complete the instructions that follow.
if ( mangle k = 82^{circ} ), find ( mangle l, mangle m ), and ( mangle n ).
a. ( mangle l = 82^{circ}, mangle m = 82^{circ}, mangle n = 98^{circ} )
b. ( mangle l = 82^{circ}, mangle m = 98^{circ}, mangle n = 98^{circ} )
c. ( mangle l = 98^{circ}, mangle m = 82^{circ}, mangle n = 98^{circ} )
d. ( mangle l = 98^{circ}, mangle m = 98^{circ}, mangle n = 82^{circ} )

Explanation:

Step1: Use the property of adjacent angles in a parallelogram

In a parallelogram, adjacent angles are supplementary. So, \(m\angle K + m\angle L=180^{\circ}\). Given \(m\angle K = 82^{\circ}\), then \(m\angle L=180^{\circ}-82^{\circ}=98^{\circ}\).

Step2: Use the property of opposite angles in a parallelogram

Opposite angles in a parallelogram are equal. So, \(m\angle K=m\angle M\) and \(m\angle L = m\angle N\). Since \(m\angle K = 82^{\circ}\), then \(m\angle M=82^{\circ}\). And since \(m\angle L = 98^{\circ}\), then \(m\angle N=98^{\circ}\).

Answer:

D. \(m\angle L = 98^{\circ},m\angle M = 82^{\circ},m\angle N = 98^{\circ}\)