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How to Find a Missing Angle in a Triangle

How to Find a Missing Angle in a Triangle

To find the missing angle of a triangle, use the fact that the interior angles of a triangle triangle add up to 180°.



If any of the angles (A, B or C) is unknown, it can be found as long as the other two angles are known.

How to Find the Missing Angle in an Equilateral Triangle

All angles in an equilateral triangles are 60°.

Any missing angle will be 60°.

Question: What is the missing angle A in the triangle below?



The triangle has 3 equal sides, so it is an equilateral triangle.

The missing angle A is 60°

How to Find the Missing Angle in an Isosceles Triangle

An isosceles triangle has two angles that are equal to each other.



There are now 2 unknowns:

  • If A is known, B can be found.

  • If B is known, A can be found.

Finding the 'Different' Angle A When the 'Repeated' Angle B Is Known


Question: What is the missing angle A in the triangle below?



Step 1: The unlabelled angle is equal to the 70° angle, because it is an isosceles triangle.



Step 2: The angles add up to 180°.
A + 70° + 70° = 180°.

Step 3: Solve the equation to find A.
A = 180° - 70° - 70° = 40°.

The missing angle A is 40°.

Finding the 'Repeated' Angle B When the 'Different' Angle A Is Known


Question: What is the missing angle B in the triangle below?



Step 1: The unlabelled angle is equal to the angle B, because it is an isosceles triangle.



Step 2: The angles add up to 180°.
30° + B + B = 180°.

Step 3: Solve the equation to find B.

30° + B + B = 30° + 2B = 180°.

2B = 180° - 30° = 150°.

B = 150° ÷ 2 = 75°.

The missing angle B is 75°.

How to Find the Missing Angle in an Isosceles Triangle

A scalene triangle has 3 different angles.



2 angles must be known if the 3rd is to be found.

Question: What is the missing angle A in the triangle below?



Step 1: The angles add up to 180°.
A + 65° + 75° = 180°.

Step 2: Solve the equation to find A.
A = 180° - 65° - 75° = 40°.

The missing angle A is 40°.
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Note

FINDING THE MISSING ANGLE BY SOLVING THE EQUATION

The interior angles of a triangle always add up to 180°.



where A, B and C are the interior angles of a triangle.



is an algebraic equation.

It can be rearranged to make A, B or C the subject of the equation.

By recognising that it is algebraic equaiton that contains addition, take the terms representing the known angles to the other side of the equation by subtracting them from both sides:



  • Label each angle in the triangle with a letter.

  • The unknown letter will be to the left of the =.

  • Insert the values of the known letters into the right hand side of the equation.

  • Calculate the unknown angle.
This method will always work.

However, the different types of triangles have some slightly different implications for the method.