Question

If m <L=m <K and m <J=20 what is the measure of the exterior angle at vertex K

Answer 1

Answer:

$100^{\circ}$

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.

$m\angle J+m\angle K+m\angle L=180^{\circ}$

$20^{\circ}+m\angle K+m\angle L=180^{\circ}$

$20^{\circ}-20^{\circ}+m\angle K+m\angle L=180^{\circ}-20^{\circ}$

$m\angle K+m\angle L=160^{\circ}$

Since $m\angle L=m\angle K$, so using substitution property of equality we will get,

$m\angle L+m\angle L=160^{\circ}$

$2*m\angle L=160^{\circ}$

$\frac{2*m\angle L}{2}=\frac{160^{\circ}}{2}$

$m\angle L=80^{\circ}$

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.

$\text{Exterior angle at vertex K}=20^{\circ}+80^{\circ}$

$\text{Exterior angle at vertex K}=100^{\circ}$

Therefore, the measure of the exterior angle at vertex K is 100 degrees.

Answer 2

The angle measurement is 70