Answer:
The measure of the largest interior angle is [tex]87.5^{o}[/tex].
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 [tex]180^{o}[/tex].
So that;
b + c + 40° = [tex]180^{o}[/tex]
b + c = [tex]180^{o}[/tex] - 40°
b + c = [tex]140^{o}[/tex]
But, b and c are in the ratio 3:5
Thus,
b = [tex]\frac{3}{8}[/tex] x [tex]140^{o}[/tex]
= [tex]52.5^{o}[/tex]
b = [tex]52.5^{o}[/tex]
c = [tex]\frac{5}{8}[/tex] x [tex]140^{o}[/tex]
= [tex]87.5^{o}[/tex]
c = [tex]87.5^{o}[/tex]
Check:
[tex]52.5^{o}[/tex] + [tex]87.5^{o}[/tex] = [tex]140^{o}[/tex]
The measure of the largest interior angle is [tex]87.5^{o}[/tex].
