Geometry

• What will you learn in today's video?

  You will learn how to get the measures of angles in any polygons.
• What is the sum of the interior angles of a triangle?

  The sum of the interior angles of a triangle is 180°.
• What types of triangles are mentioned in the video?

  Equilateral, right, and scalene triangles.
• Why is the sum of the interior angles of a triangle important?

  It serves as the basis for calculating the sum of interior angles of other polygons.
• How do you calculate the sum of interior angles of a polygon?

  • Identify the number of sides (N).
  • Calculate the number of triangles (T) using the formula \( T = N - 2 \).
  • Multiply the number of triangles by 180°: \( \text{Sum of interior angles} = 180° \times T \).
• What is the sum of the interior angles of a quadrilateral?

  The sum of the interior angles of a quadrilateral is 360°.
• How many triangles can be formed in a quadrilateral by drawing diagonals from one vertex?

  Two triangles can be formed.
• If a polygon has five sides, how many triangles can be formed?

  Three triangles can be formed.
• What is the sum of the interior angles of a pentagon?

  The sum of the interior angles of a pentagon is 540°.
• What is the sum of the interior angles of a hexagon?

  The sum of the interior angles of a hexagon is 720°.
• What is the sum of the interior angles of a heptagon?

  The sum of the interior angles of a heptagon is 900°.
• What is the formula for calculating the sum of interior angles of any polygon?

  • Formula: \( \text{Sum of interior angles} = 180° \times (N - 2) \)
  • Where \( N \) is the number of sides.
• What is the sum of the exterior angles of any polygon?

  The sum of the exterior angles of any polygon is 360°.
• How do you find the measure of an individual exterior angle of a regular polygon?

  Divide 360° by the number of sides.
• What is the measure of an individual exterior angle of a regular 32-gon?

  11.25°.
• How do you find the measure of an individual interior angle of a regular polygon?

  Divide the sum of interior angles by the number of sides.
• What is the measure of an individual interior angle of a regular 32-gon?

  168.75°.
• How do you find the value of a missing angle in a polygon?

  Subtract the sum of known angles from the total sum of interior angles.
• What is the sum of the interior angles of a nonagon?

  The sum of the interior angles of a nonagon is 1260°.
• What is the sum of the interior angles of a dodecagon?

  The sum of the interior angles of a dodecagon is 1800°.
• What is the sum of the interior angles of a regular 45-gon?

  The sum of the interior angles of a regular 45-gon is 7740°.
• What is the measure of an individual interior angle of a regular 45-gon?

  172°.
• What is the measure of the missing angle in a quadrilateral if the known angles are 64°, 90°, and 90°?

  The missing angle is 116°.
• What are the steps to find the value of a missing angle in a polygon?

  1. Calculate the sum of interior angles using \( 180° \times (N - 2) \).
  2. Add all known angles.
  3. Subtract the sum of known angles from the total sum to find the missing angle.