Triangle and Polygon Properties

The video tutorial covers various geometric concepts, including the calculation of interior angles in polygons, the properties of regular polygons, and the determination of polygon sides. It also explores quadrilaterals, the triangle inequality theorem, and exterior angles in triangles. The isosceles triangle theorem and its converse are discussed, providing a comprehensive review of these geometric principles.

What is the formula to calculate the sum of interior angles of a polygon with n sides?

• (n - 2) * 180

• (n + 2) * 180

• n * 360

• n * 180

If a regular decagon has a total interior angle sum of 1440 degrees, what is the measure of each interior angle?

• 180 degrees

• 160 degrees

• 144 degrees

• 120 degrees

A polygon has an interior angle sum of 3240 degrees. How many sides does it have?

• 18

• 20

• 22

• 24

What is the total sum of the interior angles of a regular polygon if one interior angle measures 135 degrees?

• 1080 degrees

• 1440 degrees

• 1620 degrees

• 1260 degrees

What is the best name for a polygon with four sides?

• Hexagon

• Pentagon

• Quadrilateral

• Triangle

Can a triangle be formed with side lengths of 5, 5, and 9?

• Yes, because the sum of any two sides is greater than the third side.

• No, because the sum of any two sides is not greater than the third side.

• Yes, because all sides are equal.

• No, because one side is longer than the sum of the other two.

What is the largest possible perimeter of a triangle with side lengths 5, 12, and x, where x is less than 20?

• 36.99

• 38.99

• 37.99

• 39.99

Which angles are considered exterior angles in triangle MLT?

• Angles 2 and 5

• Angles 4 and 5

• Angles 1 and 2

• Angles 3 and 4

Using the exterior angle theorem, what is the measure of angle PQR if the exterior angle is 11x + 24?

• 124 degrees

• 112 degrees

• 100 degrees

• 136 degrees

What does the converse of the isosceles triangle theorem state?

• If a triangle is equilateral, then it is also equiangular.

• If a triangle is equiangular, then it is also equilateral.

• If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

• If two sides of a triangle are congruent, then the angles opposite those sides are congruent.