Triangle Classification Using Angles — Practice Geometry Questions

By Allen Ma, Amber Kuang

You can identify triangles by their angle measurements. Using the fact that all angles in a triangle add up to 180 degrees, you apply some algebra to determine whether a triangle is equiangular, isosceles, scalene, right, acute, or obtuse.

Practice questions

Triangle WXY is drawn with

image0.png

extended to

image1.png

Use the diagram and the given information to classify each triangle as acute, obtuse, equiangular, or right.

image2.png

  1. image3.png

    is 20 more than

    image4.png

  2. image5.png

    is 30 more than twice

    image6.png

Answers and explanations

  1. Acute

    Write down the given angle measures:

    image7.png

    The sum of the three angles of a triangle is 180 degrees:

    image8.png

    Find the measure of each angle by plugging in 55 degrees for x:

    image9.png

    Because the largest angle of this triangle is less than 90 degrees, this triangle is acute.

  2. Right

    image10.png

    These two angles form a linear pair, so they add up to 180 degrees. Use these relationships to solve for x and find

    image11.png

    Therefore,

    image12.png

    With this info and the given

    image13.png

    find the measure of the remaining angle in the triangle:

    image14.png

    If one angle in the triangle is 90 degrees, then the triangle is a right triangle.