Triangle Classification Using Angles — Practice Geometry Questions

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

extended to

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

1. 

   is 20 more than

   

2. 

   is 30 more than twice

   

Answers and explanations

1. Acute

   Write down the given angle measures:

   

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

   

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

   

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

2. Right

   

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

   

   Therefore,

   

   With this info and the given

   

   find the measure of the remaining angle in the triangle:

   

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