1.
How many sides does an octagon have?
Correct Answer
E. 8
Explanation
An octagon has 8 sides.
2.
What is the interior angle sum of a hexagon in degrees?
Correct Answer
C. 720
Explanation
The interior angle sum of a polygon can be found by using the formula (n-2) * 180, where n is the number of sides of the polygon. In the case of a hexagon, which has 6 sides, the interior angle sum would be (6-2) * 180 = 4 * 180 = 720 degrees.
3.
What is the measure of one exterior angle of a regular decagon?
Correct Answer
B. 36 degrees
Explanation
The measure of one exterior angle of a regular decagon is 36 degrees. In a regular decagon, all the exterior angles are congruent, meaning they have the same measure. Since a decagon has 10 sides, the sum of all the exterior angles is 360 degrees. Therefore, each exterior angle is 360 degrees divided by 10, which equals 36 degrees.
4.
What is the measure of one interior angle of a regular pentagon?
Correct Answer
C. 108 degrees
Explanation
The measure of one interior angle of a regular pentagon is 108 degrees. In a regular polygon, all interior angles are equal. To find the measure of each angle, we can use the formula (n-2) * 180 / n, where n is the number of sides of the polygon. For a pentagon, n is 5, so the formula becomes (5-2) * 180 / 5 = 3 * 180 / 5 = 540 / 5 = 108 degrees.
5.
Which of the following is true about a regular octagon?I. - It is concave.II. - It is equilateral.III.- It is equiangular.
Correct Answer
E. II and III only
Explanation
A regular octagon is a polygon with eight sides and eight angles. It is equilateral because all of its sides have the same length. It is also equiangular because all of its angles have the same measure. However, it is not concave because all of its interior angles are less than 180 degrees, making it a convex polygon. Therefore, the correct answer is II and III only.
6.
In parallelogram ABCD shown below, angle A = 50 degrees, what is the measure of angle C?
Correct Answer
50
50 degrees
Explanation
The measure of angle C in parallelogram ABCD is also 50 degrees. This is because opposite angles in a parallelogram are congruent, meaning they have the same measure. Therefore, since angle A is 50 degrees, angle C must also be 50 degrees.
7.
In parallelogram ABCD, if angle A = 40 degrees, what is the measure of angle B?
Correct Answer
140
140 degrees
Explanation
Since opposite angles in a parallelogram are equal, angle B must also be 40 degrees. This is because angle A and angle B are opposite angles in parallelogram ABCD.
8.
In parallelogram ABCD, if the measure of angle A = 3x + 10 degrees and the measure of angle C = 4x degrees, what is x in degrees?
Correct Answer
10
10 degrees
Explanation
The angles in a parallelogram are congruent, meaning they have the same measure. Therefore, angle A and angle C must be equal. Setting the two expressions equal to each other, we can solve for x. 3x + 10 = 4x. Subtracting 3x from both sides gives 10 = x. Therefore, x is equal to 10 degrees.
9.
In parallelogram ABCD, if AB = 8x - 2 and CD = 6x + 8, what is the length of AB?
Correct Answer
38
Explanation
The length of AB can be found by equating it to 8x - 2. Since no other information is given about the parallelogram, we can assume that AB is one of the sides of the parallelogram. Therefore, the length of AB is 8x - 2, which is equal to 38.
10.
In parallelogram ABCD below, AE = 8. What is the measure of CE?
Correct Answer
8
Explanation
In a parallelogram, opposite sides are equal in length. Since AE = 8, CE must also be equal to 8.
11.
In parallelogram ABCD below, BE = 7, what is the length of BD?
Correct Answer
14
Explanation
Since BE is equal to 7, and the opposite sides of a parallelogram are equal in length, BD must also be equal to 7. Therefore, the length of BD is 14.
12.
In rectangle ABCD shown below, AC = 10x and BD = 30.What does x equal?
Correct Answer
3
Explanation
In the given rectangle ABCD, AC is equal to 10 times x and BD is equal to 30. Since AC and BD are diagonals of the rectangle, they are equal in length. Therefore, 10x = 30. Dividing both sides of the equation by 10, we get x = 3.
13.
In the rectangle shown below, find the measure of x in degrees.
Correct Answer
100
100 degrees
14.
In the rhombus below, find x if MA = 2x + 5 and AT = 3x - 2.
Correct Answer
7
Explanation
In a rhombus, opposite sides are equal. Therefore, MA = AT. Setting the given expressions equal to each other, we get 2x + 5 = 3x - 2. Solving this equation, we find x = 7.
15.
In rhombus MATH, which of the following are true?I. MT = AHII. MA = AT = TH = MHIII. MY = AY.
Correct Answer
B. II only
Explanation
In a rhombus, opposite sides are congruent. Therefore, in rhombus MATH, we can conclude that MA = AT = TH = MH. This is the only statement that is true, so the correct answer is II only.
16.
In the square below, if AE = 5, what is DE?
Correct Answer
A. 5
Explanation
Since the square has equal sides, we can conclude that DE is also equal to 5.
17.
In the square shown below, which of the following are true?I. Diagonals AC and BD are congruentII. Diagonals AC and BD are perpendicular.III. Angle BAD is a right angle.
Correct Answer
E. I, II and III
Explanation
In the given square, all the statements I, II, and III are true. Statement I is true because diagonals AC and BD are congruent since they both have the same length and intersect at their midpoints. Statement II is true because diagonals AC and BD are perpendicular to each other, forming right angles. Statement III is true because angle BAD is a right angle, as all angles in a square are right angles. Therefore, the correct answer is I, II, and III.
18.
In Isosceles Trapezoid ABCD, AB = 8x and CD = 32. Find the value of x.
Correct Answer
4
Explanation
In an isosceles trapezoid, the non-parallel sides are congruent. This means that AB = CD. Therefore, if AB = 8x and CD = 32, we can set up the equation 8x = 32 and solve for x. Dividing both sides of the equation by 8, we get x = 4.
19.
In Isosceles Trapezoid ABCD, diagonal AC = 2x + 3 and diagonal BD = 4x - 5. Find the length of AC.
Correct Answer
11
20.
What do an isosceles trapezoid and a rectangle have in common?I. congruent diagonalsII. diagonals bisect each otherIII. right angles
Correct Answer
A. I only
Explanation
An isosceles trapezoid and a rectangle have congruent diagonals in common. This means that the diagonals of both shapes have the same length.
21.
The length of one side of a square is 10 cm. Find the length of the diagonal to the nearest tenth. Hint: you can use Pythagorean Theorem or the 45-45-90 triangle created.
Correct Answer
A. 14.1
Explanation
The length of the diagonal of a square can be found using the Pythagorean Theorem. In a square, the diagonal forms a right triangle with the sides of the square. The length of one side of the square is given as 10 cm. Using the Pythagorean Theorem, we can find the length of the diagonal. The formula is d = √(a^2 + b^2), where d is the length of the diagonal, and a and b are the lengths of the sides of the square. In this case, a and b are both 10 cm. Plugging in the values, we get d = √(10^2 + 10^2) = √(200) ≈ 14.1 cm.