Question 1

Which of the following is always true for a convex polygon?

Accepted Answer

All interior angles are less than 180 degrees

Answer

It has at least one interior angle that is greater than 180 degrees

Answer

It has at least one exterior angle that is 360 degrees

Answer

All its sides are of equal length

Question 2

How can you tell if a polygon is convex?

Accepted Answer

All its interior angles are less than 180 degrees

Answer

It has at least one interior angle that is 90 degrees

Answer

All its interior angles are greater than 180 degrees

Answer

It has an odd number of sides

Question 3

A polygon can be classified as convex if:

Accepted Answer

A straight line segment connecting any two points on the interior of the polygon lies entirely inside the polygon

Answer

It has more than four sides

Answer

A straight line segment connecting any two points on the interior of the polygon lies entirely outside the polygon

Answer

One of its interior angles is obtuse

Question 4

In a convex polygon with n sides, what is the total number of triangles that can be formed by connecting any 3 non-collinear vertices?

Accepted Answer

n(n-1)(n-2)/6

Answer

n^2

Answer

3n

Answer

2n

Question 5

Which statement is true for all convex polygons?

Accepted Answer

The sum of the interior angles is equal to (n-2) × 180 degrees, where n is the number of sides

Answer

The polygon has at least one right angle

Answer

Each exterior angle is greater than 180 degrees

Answer

The sum of the interior angles is equal to n × 180 degrees, where n is the number of sides

Question 6

What is an essential property of a convex polygon?

Accepted Answer

All diagonals lie inside the polygon

Answer

The polygon has at least one side longer than the perimeter

Answer

All diagonals lie outside the polygon

Answer

It has at least one exterior angle that is greater than 180 degrees

Question 7

In a convex hexagon (six-sided polygon), what is the sum of its interior angles?

Accepted Answer

720 degrees

Answer

180 degrees

Answer

360 degrees

Answer

540 degrees

Question 8

Which of the following is a property of convex polygons?

Accepted Answer

All interior angles are less than 180 degrees

Answer

All sides have equal length

Answer

It has right angles

Answer

At least one interior angle is greater than 180 degrees

Question 9

What is the maximum number of interior right angles a convex polygon can have?

Accepted Answer

3

Answer

4

Answer

6

Answer

5

Question 10

If a convex polygon has 8 sides, what is the measure of each exterior angle?

Accepted Answer

45 degrees

Answer

90 degrees

Answer

30 degrees

Answer

60 degrees

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