Question

in △plw, m∠l = 104 and the measure of the exterior angle at p is 143. which is the shortest side of the triangle?

Explanation:

Step1: Find the measure of ∠P

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. Also, the measure of an interior angle and its adjacent exterior angle are supplementary.
So, \(m\angle P=180 - 143=37\)

Step2: Find the measure of ∠W

We know that the sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle W=x\). Then \(m\angle P+m\angle L+m\angle W = 180\)
Substitute \(m\angle P = 37\) and \(m\angle L=104\) into the equation: \(37+104+x = 180\)
\(x=180-(37 + 104)=39\)

Step3: Compare the angles

We have \(m\angle P = 37\), \(m\angle W=39\), \(m\angle L = 104\)
Since in a triangle, the side opposite the smaller angle is shorter. The smallest angle is \(\angle P\)

Step4: Identify the side opposite the smallest angle

The side opposite \(\angle P\) is \(LW\)

Answer:

\(LW\)