Question

what type of polygon has four sides?

select one:
a. quadrilateral
b. triangle
c. octagon
d. pentagon

which of the following is true for a convex polygon?

select one:
a. it always has even numbers of sides.
b. it has at least one diagonal outside the polygon.
c. at least one interior angle is greater than 180°.
d. all interior angles are less than 180°.

what is the main difference between a convex and a concave polygon?

select one:
a. a concave polygon has all diagonals inside the polygon.
b. a concave polygon has all sides equal.
c. a convex polygon has all interior angles less than 180°.
d. a convex polygon has at least one interior angle greater than 180°.

Explanation:

Identify the polygon with four sides

$$ \text{Sides} = 4 \implies \text{Quadrilateral} $$

Determine the properties of a convex polygon

$$ \forall \theta_{\text{interior}}, \theta_{\text{interior}} < 180^\circ $$

Compare convex and concave polygons

$$
LATEXBLOCK0
$$

Answer:

Question 1

• a. Quadrilateral (Correct answer)
• b. Triangle
• c. Octagon
• d. Pentagon

Question 2

• a. It always has even numbers of sides.
• b. It has at least one diagonal outside the polygon.
• c. At least one interior angle is greater than \(180^\circ\).
• d. All interior angles are less than \(180^\circ\). (Correct answer)

Question 3

• a. A concave polygon has all diagonals inside the polygon.
• b. A concave polygon has all sides equal.
• c. A convex polygon has all interior angles less than \(180^\circ\). (Correct answer)
• d. A convex polygon has at least one interior angle greater than \(180^\circ\).