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

Question

asked May 4, 2018 151k views

2 Answers

Aarkan · Answer 1 · 2018-05-09T08:29:15+0000

Answer:

$100^(\circ)$

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.