Exterior Angle Theorem of Triangles — Practice Geometry Questions

By Allen Ma, Amber Kuang

In geometry, you can use the exterior angle of a triangle to find a missing interior angle. The following practice questions ask you to do just that, and then to apply some algebra, along with the properties of an exterior angle, to find a missing variable.

Practice questions

Use the figure and the given information to answer the following questions.

image0.png

  1. In triangle WXY,

    image1.png

  2. In triangle WXY,

    image2.png

    Each angle is represented by the following:

    image3.png

    Solve for the variable b.

Answers and explanations

  1. 70 degrees

    The exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles of the triangle, so set up an equation and solve for x:

    image4.png

    Plug in the value for x to find

    image5.png

  2. 120 degrees

    The exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles of the triangle. Use this relationship to solve for a:

    image6.png

    Plug in the value of a to find

    image7.png

    The angles of a triangle add up to 180 degrees. Therefore,

    image8.png