Exterior Angles
There are two types of angles formed by triangles:
Interior Angles: The three angles inside of the triangle (they add to 180°)
Exterior Angles: The angles on the outside of the triangle, formed by extending any side of the triangle.
Exterior Angles: The angles on the outside of the triangle, formed by extending any side of the triangle.
The exterior angle and its adjacent interior angles are supplementary, so they add to 180°.
This characteristic of exterior angles can be used to find missing angles:
This characteristic of exterior angles can be used to find missing angles:
We use the angle sum property of triangles to determine the measure of angle a:
34 + 30 + a = 180
64 + a = 180
a = 116°
Angle b is supplementary to angle a:
180 - 116 = b
b = 64°
34 + 30 + a = 180
64 + a = 180
a = 116°
Angle b is supplementary to angle a:
180 - 116 = b
b = 64°
The value of the exterior angle is equal to the sum of the other two interior angles.
This can be seen in the example above;
b is equal to the sum of 30 and 34.
This is because the three interior angles add to 180°, as does the third interior angle and its adjacent exterior angles.
This can be seen in the example above;
b is equal to the sum of 30 and 34.
This is because the three interior angles add to 180°, as does the third interior angle and its adjacent exterior angles.
Find the value of the unknown variables below by using your knowledge of exterior and interior angles: