Unit 6 Polygons And Properties Of Quadrilaterals Test Version B

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.

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.

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.

In a parallelogram, opposite sides are equal in length. Since AE = 8, CE must also be equal to 8.

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.

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.

Since the square has equal sides, we can conclude that DE is also equal to 5.

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An octagon has 8 sides.

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.

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.

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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.

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.

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.

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.

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.

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.

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.

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.

An isosceles trapezoid and a rectangle have congruent diagonals in common. This means that the diagonals of both shapes have the same length.