Answer:
[tex]100^{\circ}[/tex]
Step-by-step explanation:
We have been given an image of triangle JKL. We are asked to find the measure of the exterior angle at vertex K.
Since measure of angle L is equal to measure of K, so we can find measure of these angles using angle sum property.
[tex]m\angle J+m\angle K+m\angle L=180^{\circ}[/tex]
[tex]20^{\circ}+m\angle K+m\angle L=180^{\circ}[/tex]
[tex]20^{\circ}-20^{\circ}+m\angle K+m\angle L=180^{\circ}-20^{\circ}[/tex]
[tex]m\angle K+m\angle L=160^{\circ}[/tex]
Since [tex]m\angle L=m\angle K[/tex], so using substitution property of equality we will get,
[tex]m\angle L+m\angle L=160^{\circ}[/tex]
[tex]2*m\angle L=160^{\circ}[/tex]
[tex]\frac{2*m\angle L}{2}=\frac{160^{\circ}}{2}[/tex]
[tex]m\angle L=80^{\circ}[/tex]
We know that measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles.
So the measure of exterior angle at the vertex K will be equal to measure of angle J plus measure of angle L.
[tex]\text{Exterior angle at vertex K}=20^{\circ}+80^{\circ}[/tex]
[tex]\text{Exterior angle at vertex K}=100^{\circ}[/tex]
Therefore, the measure of the exterior angle at vertex K is 100 degrees.
