Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)
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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. image3.png

    is 20 more than

  2. image5.png

    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




    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.

About This Article

This article is from the book:

About the book authors:

Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, New York. Allen, who has taught geometry for 20 years, is the math team coach and a former honors math research coordinator. Amber has taught all levels of mathematics, from algebra to calculus, for the past 14 years.

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