14. The ratio of the angles in a triangle is 3:10:7. What is the measure of the middle sized angle?

Answer 1

To find the measure of the middle sized angle in the triangle, we need to first find the total sum of the angles in a triangle, which is always 180 degrees.

Let the ratio be 3x:10x:7x, where x is a common factor for all angles.

Therefore, the sum of the angles is 3x + 10x + 7x = 20x

Since the total sum of the angles in a triangle is 180 degrees, we can set up an equation:

20x = 180

Now, solve for x:

x = 180/20
x = 9

Now, find the measure of the middle sized angle, which is 10x:

10x = 10(9) = 90

Therefore, the measure of the middle sized angle in the triangle is 90 degrees.