Question

in triangle ABC, angle A = 35 and the measure of the exterior angle at C is 100. which is the longest side of the triangle?

Answer 1

AB is the longest side

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To find the longest side of triangle ABC, we follow these steps:

Step 1: Calculate angle B using the exterior angle theorem.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. Thus:

• angle B + angle A = exterior angle at C

Given that the exterior angle at C is 100 degrees and angle A is 35 degrees, we can calculate angle B as follows:

• angle B = exterior angle at C - angle A
• angle B = 100 degrees - 35 degrees
• angle B = 65 degrees

Step 2: Calculate angle C.

We know that the sum of angles in a triangle is always 180 degrees. We already have the measures of angle A and angle B, so we can calculate angle C by subtracting the sum of angle A and angle B from 180 degrees.

• angle C = 180 degrees - angle A - angle B
• angle C = 180 degrees - 35 degrees - 65 degrees
• angle C = 80 degrees

Step 3: Identify the longest side.

In a triangle, the side opposite the largest angle is the longest side.

We have angle A = 35 degrees, angle B = 65 degrees, and angle C = 80 degrees.

Of these angles, angle C is the largest.

Therefore, the side opposite angle C, which is side AB, is the longest side of triangle ABC.