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

Answer:

The measure of the largest interior angle is $87.5^{o}$.

Step-by-step 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 = $\frac{3}{8}$ x $140^{o}$

  = $52.5^{o}$

b = $52.5^{o}$

c = $\frac{5}{8}$ 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 $87.5^{o}$.