Answer: 96 degrees.
Explanation:
All angles in a triangle add to 180 degrees.
We are given a ratio of 3:4:8 for the angles to fulfill. This essentially means that each angle must be proportional to the other two - the third angle is double the measure of the second, and the first angle is three-quarters the size of the second.
We can find the angle measures for each by adding the values in the ratio and dividing 180 by the sum:
3 + 4 + 8 = 15
180 / 15 = 12
The value of 12 is also the value of '1' in the ratio. However, we are given values of 3, 4, and 8 in the ratio, so we must multiply 12 by these values:
12 * 3 = 36
12 * 4 = 48
12 * 8 = 96
36 + 48 + 96 = 180
This triangle fulfills the ratio, and all three angles add to 180, so these angles are correct. The largest one is 96 degrees, so that is the answer.
