Find missing angles in triangles and quadrilaterals

Key notes:

Triangles

  • Sum of Angles Theorem: The sum of the interior angles in a triangle is always 180 degrees.
  • Equilateral Triangle: All three sides are equal, and all three angles are 60 degrees.
  • Isosceles Triangle: Two sides are equal, and the angles opposite those sides are equal.
  • Right Triangle: One angle is 90 degrees. The other two angles are complementary (their sum is 90 degrees).

Quadrilaterals

  • Sum of Angles Theorem: The sum of the interior angles in a quadrilateral is always 360 degrees.
  • Parallelogram: Opposite sides are parallel, and opposite angles are equal.
  • Rectangle: A parallelogram with four right angles.
  • Rhombus: A parallelogram with all four sides equal.
  • Square: A parallelogram with four right angles and all four sides equal.
  • Trapezoid: A quadrilateral with one pair of parallel sides.

Finding Missing Angles

  1. Use the appropriate theorem or property for the given figure.
  2. Set up an equation based on the sum of the angles.
  3. Solve the equation to find the missing angle.

Examples:

  • Triangle: If two angles of a triangle are 40 degrees and 70 degrees, find the third angle.
    • 40 + 70 + x = 180
    • x = 70 degrees
  • Quadrilateral: If three angles of a quadrilateral are 100 degrees, 120 degrees, and 80 degrees, find the fourth angle.
    • 100 + 120 + 80 + x = 360
    • x = 60 degrees

Learn with an example

🌀 What is the measure of the missing angle?

______°

The sum of the three angles must be 180°. The two angles you know measure 90° and 30°.

Write an equation and find the measure of the unknown angle.

90° + 30° + ? = 180°

120° + ? = 180°

? = 180° − 120°

? = 60°

The measure of the missing angle is 60°.

🌀 What is the measure of the missing angle?

____ °

The sum of the three angles must be 180°. The two angles you know measure 59° and 31°.

Write an equation and find the measure of the unknown angle.

59° + 31° + ? = 180°

90° + ? = 180°

? = 180° − 90°

? = 90°

The measure of the missing angle is 90°.

🌀 What is the measure of the missing angle?

_____ °

The sum of the four angles must be 360°. The three angles you know measure 49°, 66°, and 146°.

Write an equation and find the measure of the unknown angle.

49° + 66° + 146° + ? = 360°

261° + ? = 360°

? = 360° − 261°

? = 99°

The measure of the missing angle is 99°.

Let’s practice!🖊️