Math 8 ( Period 1)

Angles of Triangles 5-3

All triangles have interior angles that sum to 180 degrees.

An exterior angle of a triangle is supplementary to the interior angle right next to it. They form a straight angle (a straight line)

You form this exterior angle by extending one of the sides of the triangle.

The measure of any exterior angle is the SUM of the two remote interior angles.
Remote interior angles are the OTHER TWO inside angles across from the exterior angle.

If you know the ratio of the three angles of a triangle, you can use an equation to find the measurement of each angle.

For example, say you are given that the angles have a ratio of 1:2:5 ( read this 1 to 2 to 5)
Let x be an amount that each angle is multiplied by

1x + 2x + 5x = 180

8x = 180

Divide BOTH sides by 8

x = 22.5 degrees

The angles are

1(22.5) = 22.5 degrees

2(22.5) = 45 degrees

5(22.5) = 112.5 degrees

To check:  add them and check to see that the angles degrees sum to 180

22.5 + 45 + 112.5 = 180 ( YAY-- THEY DO!)