SOMA DOS ÂNGULOS EXTERNOS DE UM POLÍGONO CONVEXO \Prof. Gis/ #10

Summary

This lesson explains how to calculate the sum of external angles in convex polygons, emphasizing that the sum is always 360°. It covers examples of various polygons, including triangles, quadrilaterals, pentagons, and hexagons, illustrating how to determine each polygon’s external angles. The lesson highlights the relationship between internal and external angles, showing they are supplementary, summing to 180°. The content is reinforced with exercises, teaching students how to divide 360° by the number of sides to calculate each external angle. By the end, learners are equipped to tackle similar problems and understand the geometric properties of polygons.

Takeaways

• 😀 The sum of the external angles of any convex polygon is always 360°.
• 😀 Internal and external angles are supplementary, meaning they sum to 180°.
• 😀 For a triangle, the internal angles are 60° each, and the external angles are 120° each, summing to 360°.
• 😀 In a quadrilateral, each internal angle is 90° and the external angles are also 90°, summing to 360°.
• 😀 In a pentagon, each internal angle is 108° and the external angles are 72°, summing to 360°.
• 😀 In a hexagon, each internal angle is 120° and the external angles are 60°, summing to 360°.
• 😀 The sum of external angles of any convex polygon remains constant at 360° regardless of the number of sides.
• 😀 The number of sides of a polygon is equal to the number of external angles.
• 😀 To find the measure of an external angle of a regular polygon, divide 360° by the number of sides.
• 😀 For polygons like the dodecagon (12 sides), if the external angle is 30°, the total sum of the external angles will still be 360°.

Q & A

What is the sum of the external angles of any convex polygon?

The sum of the external angles of any convex polygon is always 360°.

What relationship exists between an internal and an external angle in a polygon?

An internal angle and an external angle in a polygon are supplementary, meaning they sum to 180°.

How can you calculate the external angle of a regular polygon?

To calculate the external angle of a regular polygon, divide 360° by the number of sides (n).

In the case of an equilateral triangle, what is the measure of each external angle?

Each external angle of an equilateral triangle measures 120°.

If each external angle of a pentagon measures 72°, what is the sum of all external angles of the pentagon?

The sum of all external angles of the pentagon is 360°, as the sum of external angles is always 360° for any convex polygon.

How do you determine the number of sides of a polygon if you know the external angle?

To determine the number of sides of a polygon, divide 360° by the measure of the external angle.

What is the measure of each internal angle in a regular hexagon?

Each internal angle of a regular hexagon measures 120°.

How do you find the internal angle of a regular polygon if you know the external angle?

To find the internal angle of a regular polygon, subtract the external angle from 180°, as they are supplementary.

In the case of an octodecagon, how would you find the measure of each external angle?

To find the measure of each external angle of an octodecagon (18-sided polygon), divide 360° by 18. This gives each external angle as 20°.

What polygon has external angles measuring 30° each?

A regular dodecagon (12-sided polygon) has external angles measuring 30° each.