What is the measures of the angles of a triangle that are in the extended ratio 2:2:8. What is the measure of the smallest angle?
12 parts of 180? each part is 15 degrees, the smallest angle is 30 degrees
This is the right answer, but its a bit confusing. just to specify 2+2+8=12 and 180 Divided by 12 is 14
so each 2 will be 30 and the 8 is 120.
but 180 divided by 12 is 15.
To find the measures of the angles of a triangle given an extended ratio, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's denote the measures of the angles as 2x, 2x, and 8x, where x is a positive constant.
According to the extended ratio, the measures of the angles are in the ratio 2:2:8. This means that for every 2 units of measure, we have 2x degrees, and for every 8 units of measure, we have 8x degrees.
The sum of the angles in a triangle is 180 degrees, so we can write the equation:
2x + 2x + 8x = 180
Combine like terms:
12x = 180
Now we solve for x by dividing both sides of the equation by 12:
x = 180/12 = 15
Now we can find the measures of the angles by substituting x = 15 back into the expressions for the angles:
Smallest angle = 2x = 2 * 15 = 30 degrees
Therefore, the measure of the smallest angle is 30 degrees.