Question 1
The sum of the interior angles of polygon is 1800 degrees. Find the number of sides in the polygon and, what do you call that polygon?
Question 2
Which statements are true about polygons? Select three options. All sides and all angles in a polygon are congruent. The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint. In a polygon, all segments with a common endpoint are collinear. If all of the sides of a convex polygon are extended, none of them will contain any points that are inside the polygon. The extension of at least one side or diagonal in a concave polygon will contain a point that is inside the polygon.
Question 3
Which statement is true?
(a) All squares are rectangles.
(b) All quadrilaterals are rectangles.
(c) All parallelograms are rectangles.
(d) All rectangles are squares.
Answer to question 1
Let us assume that the number of sides of the given polygon is nn.
The sum of its interior angles is given to be 18001800 degrees.
But the sum of interior angles of an n-sided polygon is 180(n−2)180(n−2).
So we get:
180(n−2)=1800Dividing both sides by 180,n−2=10Adding 2 on both sides,n=12180(n−2)=1800Dividing both sides by 180,n−2=10Adding 2 on both sides,n=12
Since it is a 12-sided polygon, it is called a dodecagon.
Answer to question 2
Answer to question 3
Statement a is true since a square is a special rectangle where all of the sides are equal to each other.
Statement b is false since a quadrilateral is any polygon with four sides like a trapezoid or a rhombus that are not rectangles.
Statement c is false since a rectangle is a special case of the parallelogram where the angles are right angles.
Statement d is false since there are longer sides and shorter ones that do not make it a square.