If the angles of a triangle with measures in the ratio of 5 : 6 : 7, then find the measure of the smallest angle.
(1 point)
Responses
40°
40°
50°
50°
60°
60°
70°
To find the measure of the smallest angle in a triangle with angles in the ratio of 5:6:7, we need to find the smallest angle and then divide it by the sum of the ratios (5+6+7).
Let's assume the smallest angle is x degrees.
The ratio of the smallest angle to the entire triangle's angles is 5 / (5+6+7) = 5/18.
So, the measure of the smallest angle is (5/18) * 180 degrees (since the sum of angles in a triangle is 180 degrees):
= 5/18 * 180 degrees
Simplifying:
= (5 * 180) / 18 degrees
= 900 / 18 degrees
= 50 degrees.
So, the measure of the smallest angle is 50°.