Question

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

Answer 1

the angle measurement is 70

Answer 2

`100^(\circ)`

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)`

`(2*m\angle L)/(2)=(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.