Question

An animal pen is in the shape of a triangle. One of the interior angles of the triangle is 40°. The measures of the other interior angles are in the ratio 3 ∶ 5. What are the measures of the largest interior angle? You must show your work to receive full credit.

Answer 1

The measure of the largest interior angle is
`87.5^(o)`.

Explanation:

Given one of the interior angles of the triangle = 40°. Let the other interior angles be represented by b and c.

Sum of angles in a triangle is
`180^(o)`.

So that;

b + c + 40° =
`180^(o)`

b + c =
`180^(o)` - 40°

b + c =
`140^(o)`

But, b and c are in the ratio 3:5

Thus,

b =
`(3)/(8)` x
`140^(o)`

=
`52.5^(o)`

b =
`52.5^(o)`

c =
`(5)/(8)` x
`140^(o)`

=
`87.5^(o)`

c =
`87.5^(o)`

Check:

`52.5^(o)` +
`87.5^(o)` =
`140^(o)`

The measure of the largest interior angle is
`87.5^(o)`.