Question

An exterior angle of a triangle is 140 degrees. If the non-adjacent angles are congruent, then what are the measures of all of the interior angles of the triangle?

Answer 1

The measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees

Solution:

Given that exterior angle of triangle is 140 degrees

The exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles

Given that adjacent angles are congruent

Let one of the non adjacent interior angles be "x"

x + x = 140

2x = 140

x = 70

So the two interior angles are 70 degrees and 70 degrees

Let us find the third interior angle

The angle sum property of a triangle states that the interior angles of a triangle always add up to 180 degrees

70 + 70 + third angle = 180

third angle = 180 - 70 - 70

third angle = 180 - 140

third angle = 40 degrees

Thus the measures of all of the interior angles of the triangle are 70 degrees, 70 degrees and 40 degrees