Final answer:
To find the measure of the middle angle in a triangle with angle measures in the extended ratio of 3:4:11, we can set up an equation and solve for the common factor x. Substituting x into the ratio allows us to find the measure of the middle angle.
Step-by-step explanation:
To find the measure of the middle angle of a triangle with angle measures in the extended ratio of 3:4:11, we can first find the total sum of the angles. Since a triangle has a total of 180 degrees, we can set up the equation 3x + 4x + 11x = 180, where x is a common factor. Simplifying this equation gives us 18x = 180. Dividing both sides by 18 yields x = 10.
Now, we can substitute x back into the ratio to find the measures of each angle. The middle angle is 4x, so substituting x = 10 gives us 4 * 10 = 40 degrees.
Learn more about Triangle angles