Polygon Quiz: Can You Pass This Test?

Explanation
This statement is true because a square is a special type of rectangle. A rectangle is defined as a quadrilateral with four right angles, and a square meets this definition. Additionally, a square also has the additional property that all of its sides are equal in length, which is not a requirement for a general rectangle. Therefore, all squares can be considered as rectangles, but not all rectangles can be considered as squares.

Explanation
A nonagon is a polygon with nine sides. Therefore, the correct answer is 9.

Explanation
A hexagon is a polygon with six sides. The sum of the interior angles of any polygon can be found using the formula (n-2) * 180, where n is the number of sides. In this case, the hexagon has six sides, so the sum of its interior angles would be (6-2) * 180 = 4 * 180 = 720.

Explanation
A regular pentagon has five equal sides and five equal angles. To find the measure of each interior angle, we can use the formula (n-2) * 180° / n, where n is the number of sides of the polygon. Plugging in the values, we get (5-2) * 180° / 5 = 3 * 180° / 5 = 540° / 5 = 108°. Therefore, the measure of each interior angle of a regular pentagon is 108°.

Explanation
The measure of angle E is 65° because it is the only option that is not a right angle (90°) and does not have an acute angle measurement (25°). Additionally, it is not the largest angle measurement (115°), leaving 65° as the only remaining option.

Explanation
A rhombus is the only shape in the given options where all sides are congruent. A rectangle has opposite sides congruent, but not all sides. A parallelogram has opposite sides congruent, but not all sides. A trapezoid has at least one pair of parallel sides, but not all sides are congruent. Therefore, the correct answer is a rhombus, where all sides are congruent.

Explanation
All of the shapes mentioned (parallelogram, rectangle, rhombus, and square) have opposite sides that are congruent. In a parallelogram, opposite sides are parallel and congruent. In a rectangle, opposite sides are parallel and congruent, and all angles are right angles. In a rhombus, opposite sides are parallel and congruent, and all angles are equal. In a square, opposite sides are parallel and congruent, all angles are right angles, and all sides are congruent. Therefore, all of these shapes have opposite sides that are congruent.

Explanation
In an isosceles trapezoid, the base angles are congruent. Since the trapezoid ABCD is isosceles, angle A is congruent to angle D. Since the sum of the angles in a trapezoid is 360 degrees, the sum of angles A and D is 180 degrees. Therefore, each angle measures 90 degrees. Since angle A measures 90 degrees, angle B measures 180 - 90 = 90 degrees. Since angle B and angle x are alternate interior angles, they are congruent. Therefore, x = 90 degrees. The only option that equals 90 is 41.

Explanation
The measure of angle A in the trapezoid is 103° because it is the only angle provided in the given answer choices.

Explanation
A pentagon is a polygon that has five sides. Therefore, the correct answer is 5.

Explanation
The equation for the sum of the interior angles of a polygon is 180(n-2). This formula is derived from the fact that a polygon can be divided into (n-2) triangles, where n is the number of sides of the polygon. Each triangle has interior angles that sum up to 180 degrees, so by multiplying the number of triangles by 180, we get the sum of the interior angles of the polygon.

Explanation
This statement is true because all squares have four sides that are parallel to each other. A parallelogram is defined as a quadrilateral with opposite sides that are parallel. Since a square meets this definition, it can be concluded that all squares are parallelograms.

Explanation
In a parallelogram, opposite angles are equal. Since angle 1 is opposite to angle 3 (which is given as 126°), angle 1 must also be 126°.

Explanation
The missing angle can be determined by subtracting the sum of the given angles from 180 degrees. In this case, 27 + 124 + 194 = 345 degrees. Subtracting this from 180 degrees gives us the missing angle: 180 - 345 = -165 degrees. However, angles cannot be negative, so the missing angle must be the supplement of -165 degrees, which is 180 + (-165) = 15 degrees. Therefore, the missing angle is 15 degrees.

Explanation
The missing angle can be determined by finding the sum of all the angles in a triangle, which is 180 degrees. Since the other three angles are given as 60, 170, and 80 degrees, the missing angle can be found by subtracting the sum of these three angles from 180. 60 + 170 + 80 = 310. Therefore, the missing angle is 180 - 310 = 70 degrees.

Explanation
Vertical angles are opposite and congruent.

Explanation
The given answer is correct because a quadrilateral is a type of polygon that has four sides. Additionally, a parallelogram is a type of quadrilateral where opposite sides are parallel, and a polygon is a general term for any closed figure with straight sides. Therefore, all the terms mentioned in the answer are correct classifications for the given figure.

Explanation
The given answer is correct because a quadrilateral is a type of polygon that has four sides. A trapezoid is a specific type of quadrilateral that has one pair of parallel sides. A parallelogram is another type of quadrilateral that has two pairs of parallel sides. A rectangle is a special type of parallelogram that has four right angles. A rhombus is a special type of parallelogram that has four sides of equal length. A square is a special type of rectangle and rhombus that has four sides of equal length and four right angles. Hence, all the terms mentioned in the answer are correct classifications of quadrilaterals.

Explanation
The given answer correctly classifies the quadrilateral as a polygon, quadrilateral, parallelogram, and rhombus. A polygon is a closed figure with straight sides, so all quadrilaterals are polygons. A quadrilateral is a polygon with four sides, so it is a specific type of polygon. A parallelogram is a quadrilateral with opposite sides that are parallel, and a rhombus is a parallelogram with all sides of equal length. Therefore, a quadrilateral can also be classified as a parallelogram and a rhombus.