Final answer:
The smallest angle of a triangle with angle measures in the ratio 4:8:6 is 40 degrees. We determine this by applying the fact that the sum of the angles in a triangle is 180 degrees and calculating the value of each part of the ratio.
Step-by-step explanation:
The question 'What is the measure of the smallest angle?' deals with understanding the properties of triangles and how to work with ratios. Since the sum of the angles in any triangle is always 180 degrees, we can use the given ratio of 4:8:6 to find the measures of the individual angles. First, add the parts of the ratio: 4 + 8 + 6 = 18. Next, we know that 18 parts are equal to 180 degrees, so each part is equal to 180 ÷ 18, which equals 10 degrees.
Now, multiply each part of the ratio by 10 to find the measure of each angle:
- 4 parts × 10 degrees per part = 40 degrees
- 8 parts × 10 degrees per part = 80 degrees
- 6 parts × 10 degrees per part = 60 degrees
The smallest angle then corresponds to 4 parts, which is 40 degrees. Hence, the correct answer is C. 40 degrees.