Angles That Form Linear Pairs—Practice Geometry Questions

By Allen Ma, Amber Kuang

Angles that form a linear pair combine to form a straight angle. (A straight angle measures 180 degrees.) The following practice questions ask you to solve problems based on linear pairs.

Practice questions

In the following figure,

image0.png

at E. In the following questions, fill in the blank to make the statement true.

image1.png

  1. If you know that

    image2.png

    are represented by 2a, 2a + b, and 3a – 20, respectively then b = ———?

  2. If you know that

    image3.png

Answers and explanations

  1. 20

    Start with the given information:

    image4.png

    form a linear pair, which means their sum is 180 degrees. Set up the following equation and solve for a:

    image5.png

    Plug in the value of a to find

    image6.png

    because they’re vertical angles. Set them equal to each other, plug in the value of a, and solve for b:

    image7.png

  2. 124 degrees

    Angles that form a linear pair add up to 180 degrees. Set the sum of

    image8.png

    equal to 180 and solve for x:

    image9.png

    Now plug in the value of x to solve for

    image10.png