Question

The measures of the angles of a triangle are in the extended ratio 2:2:8. What is the measure of the smallest angle?

Answer 1

We know that the ratio is;

$2:2:8$

The angles in a triangle add up to give 180°

We can think of there being twelve "parts" that add up to 180°

$2x + 2x + 8x = 180 \\ \\ 12x = 180 \\ \\ x = \frac{180}{12} \\ \\ x = 15$

So our ratio is;

$2*15 : 2*15 : 8*15 \\ \\ = 30 : 30 :120$

So the smallest angle is 30°

Answer 2

Let the three angles of the triangle be represented by 2x, 2x, and 8x.

2x + 2x + 8x = 180

x = 15 and 2x = 30.

The angles of the triangle are 30, 30, and 120.

The smallest angle has measure 30.

Note that  30:30:120 is equivalent to the given ration 2:2:8