How to Find the Measure of an Angle

Two rays that have the same endpoint create an angle. The point at which they intersect is called the vertex. The angle forms part of an imaginary circle. And, since circles measure 360-degrees, you can find the angle measurement formed by the rays. Here are some things that you should know about how to find the measure of an angle.

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Four Types of Angles

There are four types of angles. Knowing the difference helps you estimate the measurement of an angle. Here are the four types of angles and the measurements to help you classify each one.

  • Straight angle (180-degrees)
  • Acute angle (less than 90-degrees)
  • Right angle (90-degrees)
  • Obtuse angle (More than 90-degrees but less than 180 degrees)
  • Using a Protractor

    The best way to measure an angle is to use a protractor. To do this, you’ll start by lining up one ray along the 0-degree line on the protractor. Then, line up the vertex with the midpoint of the protractor. Follow the second ray to determine the angle’s measurement to the nearest degree.

    Angles in Triangles

    Triangles received their name from the three angles that they possess. These three angles should add up to 180-degrees. Oftentimes, you’ll have the measurements of two angles. However, you’ll have to figure out the measurement of the third angle. The equation to use is:

    angle A + angle B + angle C = 180-degrees.

    For example, say you have the following triangle. What is the measurement of angle C?

    how to find the measure of an angle, illustration example A - magoosh

    If you plug these numbers into the equation, you get the following equation:

    angle measurement, work out example A - magoosh

    Angles in Quadrilaterals

    Squares and rectangles have four right angles. If you add up the angles, you get 90 + 90 + 90 + 90 = 360. A quadrilateral also has four angles. Therefore, the shape’s angles add up to 360-degrees even if there are no right angles. To determine the missing angle of a quadrilateral, you can use the following equation:

    angle A + angle B + angle C + angle D = 360-degrees.

    Check out the following example. Can you figure out the missing angle in this quadrilateral?

    how to find the measurement of an angle, find angle in quadrilateral - magoosh

    To find the missing angle, plug the angle measurements into the equation:

    how to find the measurement of an angle, solve equation to find angle in a quadrilateral - magoosh

    Whether you’re working with a ray, triangle, or quadrilateral, there are methods you can use to discover the missing measurement of an angle. If you’re wondering how to find the measure of an angle on a ray, triangle, or quadrilateral, try using a protractor or the equations we’ve discussed. They should work, and help make your life a little easier!

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    • Jamie Goodwin

      Jamie graduated from Brigham Young University- Idaho with a degree in English Education. She spent several years teaching and tutoring students at the elementary, high school, and college level. She currently works as a contract writer and curriculum developer for online education courses. In her free time, she enjoys running and spending time with her boys!

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