The measures of the angles of a triangle are in the extended ratio 2 : 2: 8. What is the measure of the smallest angle?
can someone pretty please show me how to do this?
let the angles be 2x, 2x, and 8x
2x + 2x + 8x = 180
12x = 180
x = 15
so the angles are 30, 30 , and 120°
of course the smallest angle would be 30°
Sure! To solve this problem, we'll first need to find the sum of the ratios 2:2:8. The sum of the ratios is 2+2+8 = 12.
To find the measure of each angle, we'll divide each ratio by the sum of all the ratios and then multiply by 180 degrees (since the sum of the angles in a triangle is always 180 degrees).
Let's start with the smallest angle. The ratio for the smallest angle is 2. So we'll divide 2 by 12 and multiply by 180:
(2/12) * 180 = 30 degrees.
Therefore, the measure of the smallest angle in the triangle is 30 degrees.