Question

In the diagram of △KLM below, m∠L=70, m∠M=50, and MK is extended through N.What is the measure of ∠LKN?

Answer 1

Let's begin by listing out the information given to us:

The figure before us is triangle. It is worth noting that the sum of angles in a triangle is 180 degrees

$\begin{gathered} m\angle L=70^{\circ} \\ m\angle M=50^{\circ} \end{gathered}$

To find the angle at K (m∠LKM), we will subtract the sum of angles L & M from 180 degrees (the sum of angles in a triangle). We have:

$\begin{gathered} m\angle LKM=180-(m\angle L+m\angle M) \\ m\angle LKM=180-(70+50)=180-120=60 \\ m\angle LKM=60^{\circ} \end{gathered}$

To find the angle at LKN (m∠LKN), we will subtract angle LKM from 180 degrees (the sum of angles on a straight line). We have:

$\begin{gathered} m\angle LKN+m\angle LKM=180^{\circ} \\ m\angle LKM=60^{\circ} \\ m\angle LKN+60=180 \\ m\angle LKN=180-60=120 \\ m\angle LKN=120^{\circ} \end{gathered}$

Therefore, m∠LKN is equal to 120 degrees