The exterior angles of a triangle are in the ratio \(3:5:7\). What is the measure (in degrees) of the least interior angle of the triangle?
\(\phantom{3:4:5}\)
+2666 Note that the exterior angles will always sum to \(360^ \circ\).
The ratio also has 15 "parts", meaning each part is \(360 \div 15 = 24\)
The smallest interior angle will always be supplementary to the largest exterior angle, which is \(7 \times 24 = 168\).
This means that the smallest interior angle is \(180 - 168 = \color{brown}\boxed{12}\)
+2666 Note that the exterior angles will always sum to \(360^ \circ\).
The ratio also has 15 "parts", meaning each part is \(360 \div 15 = 24\)
The smallest interior angle will always be supplementary to the largest exterior angle, which is \(7 \times 24 = 168\).
This means that the smallest interior angle is \(180 - 168 = \color{brown}\boxed{12}\)
