In a certain triangle, the exterior angles are in the ratio $3:5:10.$ What is the measure of the smallest interior angle of the triangle, in degrees?

kittykat Jan 11, 2024

#1**+1 **

We know that the angles of the triangle are in the ratio 3:5:10, and we know that the sum of the three interior angles of a triangle is 180°, so we can do:

\(3x + 5x + 10x = 180°\)

\(18x=180°\)

\(x=10°\)

We can now multiply 3, the smallest interior angle, by x.

\(3\cdot 10\)

\(30°\)

Answer: 30°

DS2011 Jan 11, 2024