Angle Properties - Find the Angle Problems

These lessons give a summary of the different angle properties and how they can be used to find missing angles.

Related Pages
Pairs Of Angles
Corresponding Angles
Alternate Interior Angles & Alternate External Angles
More Geometry Lessons

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“Find the angle” problems are very common in tests like the SAT, GRE or the GCSE. In such problems, you will be given some lines and angles and you will be required to find a particular angle or angles.

In order to answer this type of questions,

  • you would need to know some commonly used angle properties.
  • you would need to practice lots of such problems. The more you practice, the easier it becomes to “see” which properties need to be applied.

Some Common Angle Properties

The sum of angles at a point is 360˚.

sum of angles at a point

Vertical angles are equal.

vertical angles

The sum of complementary angles is 90˚.

complementary angles

The sum of angles on a straight line is 180˚.

angles in a straight line

Alternate Angles
(Angles found in a Z-shaped figure)

Alternate angles Z

Corresponding Angles
(Angles found in a F-shaped figure)

Corresponding angles F

Interior Angles
(Angles found in a C-shaped or U-shaped figure)
Interior angles are supplementary. Supplementary angles are angles that add up to 180˚.

Interior angles C

The sum of angles in a triangle is 180˚.

Sum of angles in triangle

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Exterior angle of triangle

The sum of interior angles of a quadrilateral is 360˚.

Interior angles of quadrilateral

How to use the above angle properties to solve some “find the angle” problems?

Find the Measure of the Missing Angle

Angles and Parallel Lines : solving problems

Finding missing angles on two parallel lines, using corresponding angles and angles in a triangle.

Angles formed by Parallel Lines and Transversals

How to use Properties of Vertical Angles, Corresponding Angles, Interior Angles of a Triangle, and Supplementary Angles to find all the angles in a diagram. Other Properties discussed include Alternate Interior Angles, Alternate Exterior Angles, Complementary Angles, and the Exterior and Opposite Interior Angles of a triangle.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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