Question

(a) problem 12: (first taught in lesson 49) in \\( \triangle jfr, m \angle j = 35 \\) and the measure of the exterior angle at f is 115. which is the longest side of the triangle? after you enter your answer press go.

Explanation:

Step1: Find the measure of ∠F

The measure of an interior angle and its exterior angle add up to \(180^{\circ}\).
If the exterior angle at \(F\) is \(115^{\circ}\), then \(m\angle F=180 - 115=65^{\circ}\)

Step2: Find the measure of ∠R

The sum of the interior angles of a triangle is \(180^{\circ}\).
We know \(m\angle J = 35^{\circ}\) and \(m\angle F=65^{\circ}\). Let \(m\angle R=x\). Then \(35 + 65+x=180\), so \(x=180-(35 + 65)=80^{\circ}\)

Step3: Relate angles and sides

In a triangle, the larger the angle, the longer the side opposite it.
Since \(m\angle R = 80^{\circ}\), \(m\angle F=65^{\circ}\), \(m\angle J = 35^{\circ}\), and the side opposite \(\angle R\) is \(JF\)

Answer:

\(JF\)