The exterior angles of a triangle have measures of (x+10) degrees, (2x+20) and 3x degrees. what is the measure of the smallest interior angle of the triangle ... ?

Question

Danielle Bird

Mathematics

20 November, 01:10

The exterior angles of a triangle have measures of (x+10) degrees, (2x+20) and 3x degrees. what is the measure of the smallest interior angle of the triangle ... ?

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Haylee Huffman · Answer 1

The sum of exterior angles of any polygon will always equate to 360 degrees. Therefore, we can write:

360 = (x+10) + (2x+20) + 3x

Solving for x,

x = 55

The exterior angles will have values of 65, 130 and 165. The exterior that will have the largest value will correspond to the smallest interior angle and will have a value of 15 degrees.