Maths Quadrilaterals part 11 (Questions) CBSE Class 8 Mathematics VIII

TL;DR

This video explains how to find the measure of exterior angles in regular polygons and determine the number of sides based on interior angles.

Transcript

hello friends this video on quadrilaterals part 11 is brought to you by exam feel calm no more fear from exam question number 8 find the measure of each exterior angle of a regular polygon of nine sides of fifteen sides so we have learned that the sum of the exterior angles for any polygon doesn't matter how many sides are present in that polygon s... Read More

Key Insights

• 🍹 The sum of the exterior angles in any polygon is always 360 degrees.
• 🙃 The measure of each exterior angle in a regular polygon can be found by dividing 360 by the number of sides.
• 🙃 The sum of the interior angles in a regular polygon can be calculated using the formula (number of sides - 2) * 180 degrees.
• 🔺 By equating the given interior angle to the sum of interior angles formula, the number of sides of a regular polygon can be determined.
• 🟰 Regular polygons have equal side lengths and equal interior angles.
• 🔺 Exterior angles and interior angles are supplementary angles.
• 🔺 The number of sides in a regular polygon can be found using the formula (sum of interior angles / measure of each interior angle) + 2.

Questions & Answers

Q: How can we find the measure of each exterior angle in a regular polygon?

The measure of each exterior angle in a regular polygon can be found by dividing 360 by the number of sides. For example, if a polygon has 9 sides, each exterior angle would measure 40 degrees.

Q: If each interior angle of a regular polygon is 165 degrees, how many sides does the polygon have?

To find the number of sides, we equate the given interior angle (165 degrees) to the formula for sum of interior angles [(number of sides - 2) * 180 degrees]. Solving this equation, we find that the polygon has 24 sides.

Q: Is it possible to have a regular polygon with each exterior angle as 22 degrees?

No, it is not possible to have a regular polygon with each exterior angle as 22 degrees. This is because the sum of the exterior angles in any polygon is always 360 degrees, and 360 divided by 22 does not result in a whole number.

Q: Can the interior angle of a regular polygon be 22 degrees?

No, the interior angle of a regular polygon cannot be 22 degrees either. The sum of the interior angles formula (n-2) * 180 degrees is used to determine the sum of interior angles. Equating this formula to the given interior angle (22 degrees), we find that it is not possible to have a regular polygon with an interior angle of 22 degrees.

Summary & Key Takeaways

• The sum of the exterior angles in any polygon, regardless of the number of sides, is always 360 degrees.

• To find the measure of each exterior angle in a regular polygon, divide 360 by the number of sides.

• The sum of the interior angles in a regular polygon with X sides can be calculated using the formula (X-2) * 180 degrees.

• By equating the given interior angle(s) to the sum of the interior angles formula, the number of sides can be determined.