Question

analyze the diagram below and complete the instructions that follow.

if ( mangle l = 2(mangle m) ), find ( mangle k ) and ( mangle n ).

a. ( mangle k = 55^{circ}, mangle n = 110^{circ} )
b. ( mangle k = 60^{circ}, mangle n = 100^{circ} )
c. ( mangle k = 60^{circ}, mangle n = 120^{circ} )
d. ( mangle k = 75^{circ}, mangle n = 105^{circ} )

Explanation:

Step1: Use the property of parallelogram adjacent angles

In a parallelogram \(KLMN\), \(L\parallel MN\) and \(KL\parallel MN\). Adjacent angles of a parallelogram are supplementary, so \(m\angle L + m\angle M=180^{\circ}\). Given \(m\angle L = 2(m\angle M)\), substitute into the equation: \(2m\angle M+m\angle M = 180^{\circ}\).

Step2: Solve for \(m\angle M\)

Combine like - terms: \(3m\angle M=180^{\circ}\), then \(m\angle M = 60^{\circ}\).

Step3: Find \(m\angle L\)

Since \(m\angle L = 2(m\angle M)\), \(m\angle L=2\times60^{\circ}=120^{\circ}\).

Step4: Use the property of parallelogram opposite angles

In a parallelogram, opposite angles are equal. So \(m\angle K=m\angle M = 60^{\circ}\) and \(m\angle N=m\angle L=120^{\circ}\).

Answer:

C. \(m\angle K = 60^{\circ},m\angle N = 120^{\circ}\)