How do you solve the exterior and interior angles of a triangle?

Question

If there are 2 interior angles in a triangle, (p) and (p+15), and the 3rd interior angle is unknown, and the exterior angle that is given is (2p + 15), how can we find the exterior angle and the unknown interior angle or is it possible to solve these with the given information?

Answer 1

The exterior angle could be one of three exterior angles not necessarily adjacent to the third angle. We name the third interior angle to be x, so we have:

p + (p + 15) + x = 180

2p + 15 + x = 180

x = 165 - 2p

We have two variables and one equation, to find both variables we need two equations.

At least one of these equations is correct:

a ) 2p + 15 = p + (p + 15) => 2p + 15 = 2p + 15 always correct

b ) 2p + 15 = p + x => x = p + 15

c ) 2p + 15 = (p + 15) + x => x = p

If expression (b) is correct :

x = 165 - 2p

x = p + 15

==> 165 - 2p = p + 15 => 3p = 150 => p = 50 , x = 65

The angles are x , p , p+15: 65, 50, 65

The exterior angle measure is 2p + 15 = 2(50)+15= 115 and it is supplementary to 65 and is acceptable.

If expression (c) is correct :

x = 165 - 2p

x = p

==> 165 - 2p = p => 3p = 165 => p = 55 , x = 55

The angles are x , p , p+15: 55, 55, 65

The exterior angle measure is 2p + 15 = 2(55)+15= 125 and it is supplementary to 55 and is acceptable.

Answer 2

The measure of the exterior angle is equal to the sum of the measures of the two remote interior angles.

If the two interior angles are remote (not stated in the problem or missing diagram!), then

2p + 15 = p + p + 15, that is a trivial case.

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