Question

Given a scalene triangle with whole number angle measurements, what is the greatest sum possible of the two smallest angles?

Answer 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define scalene triangle

A Scalene Triangle is any triangle with unequal sides. This means that, in a scalene triangle, all of the three sides and angles are different lengths, just like in the illustration below. This also means that each angle has to be different.

STEP 2: Get the greatest sum possible of the two smallest angles

Since the measures of the angles of the triangle are different whole numbers , for the sum of the two angles to be the least possible, one of the angles must be smallest whole number i.e 1°

Now, the next smallest angle will be the next angle of a whole number that is not 1 degree, i.e, 2 degrees.

Thus, the greatest possible sum of the measures of two smallest angles will be:

$1^{\circ}+2^{\circ}=3^{\circ}$

Hence, the greatest sum possible of the two smallest angles is 3 degrees