Interior and Exterior Angles of Triangles | Definition & Examples

Summary

The script explains the concepts of interior and exterior angles in triangles, highlighting that interior angles always sum to 180°, while exterior angles of any polygon total 360°. Through clear examples, it demonstrates how to calculate unknown interior angles by subtraction and how exterior angles relate to their adjacent interior angles as supplements. It also introduces the triangle exterior angle theorem, showing that an exterior angle equals the sum of its two opposite interior angles and is always greater than either. The lesson concludes with guided practice to reinforce these geometric principles.

Takeaways

• 😀 Triangles have both interior and exterior angles.
• 😀 The three interior angles of any triangle always add up to 180°.
• 😀 To calculate an unknown interior angle, subtract the known angles from 180°.
• 😀 Example: If a triangle has angles of 68° and 34°, subtract both from 180° to find the third angle, which is 78°.
• 😀 The sum of all exterior angles of any polygon, including triangles, is always 360°.
• 😀 An exterior angle of a triangle is the supplement (180° minus) of its adjacent interior angle.
• 😀 Reflex angles (greater than 180° but less than 360°) are not considered when calculating exterior angles of a triangle.
• 😀 The exterior angle of a triangle is equal to the sum of the opposite interior angles.
• 😀 The exterior angle of a triangle is always greater than either of the opposite interior angles.
• 😀 To calculate the exterior angles of a triangle, subtract each interior angle from 180°.
• 😀 Check your exterior angle calculations by ensuring that the sum of all exterior angles equals 360°.

Q & A

What are the interior angles of a triangle?

The interior angles of a triangle are the three angles created at the vertices or corners of the triangle, inside the shape. These angles always add up to 180°.

How can we calculate the unknown interior angle of a triangle?

To calculate an unknown interior angle of a triangle, subtract the known angles from 180°. For example, if you know two angles, subtract their sum from 180° to find the third angle.

What is the sum of the interior angles of a triangle?

The sum of the interior angles of any triangle is always 180°.

In the triangle JOY, if angle J is 68° and angle O is 34°, what is angle Y?

To calculate angle Y, subtract the sum of angles J and O from 180°. So, 180° - 68° - 34° = 78°. Therefore, angle Y is 78°.

What is the sum of the exterior angles of any polygon, including triangles?

The sum of the exterior angles of any polygon, including triangles, is always 360°.

What are exterior angles of a triangle?

Exterior angles of a triangle are formed when one side of the triangle is extended. They are supplementary to the adjacent interior angle, meaning the sum of the exterior and the adjacent interior angle is 180°.

How do you calculate an exterior angle of a triangle?

To calculate an exterior angle of a triangle, subtract the interior angle from 180°. For example, if an interior angle is 68°, the exterior angle would be 180° - 68° = 112°.

What is the triangle exterior angle theorem?

The triangle exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Why don't exterior angles of a triangle take into account the reflex angle?

Exterior angles do not account for reflex angles because the triangle exterior angle theorem is based on the exterior angle being supplementary to the adjacent interior angle, and reflex angles would disrupt this relationship.

How can you check if your exterior angles are calculated correctly?

To check if your exterior angles are calculated correctly, add all three exterior angles of the triangle together. They should always sum to 360°.