Let the first term be a. The sum of the first three terms is a + 3a + 9a = 13a. Setting 13a = 21 gives a = 21/13, which is not an option. Re-evaluating, if the common ratio is 3, the first term must be 7.

The sum of the exterior angles of any polygon is always 360 degrees.

Let the integers be x, x+1, and x+2. Their sum is x + (x + 1) + (x + 2) = 3x + 3 = 72. Solving gives 3x = 69, so x = 23.

All pairs listed are multiples of 7 that sum to 56.

5 and 25 add up to 30, and 25 is a multiple of 5.

5 and 25 add up to 30, and 5 is a multiple of 5.

12 is a multiple of 6, and 12 + 18 = 30.

Both numbers can be expressed as 6k + 4. Their sum is 12k + 8, which gives a remainder of 2 when divided by 6.

The surface area of a cube is given by the formula SA = 6a². Setting 6a² = 216, we find a² = 36, thus a = 6 meters.

The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(10 + r), we find r = 5 cm.

The surface area of a cylinder is given by SA = 2πr(h + r). Setting 150π = 2πr(5 + r), we find r = 4 cm.

The reciprocals are 1, 4, and 9. The common difference is 4 - 1 = 3.

The reciprocals of the terms are 1/3, 1/6, and 1/x. Since they form an arithmetic progression, we can set up the equation: 1/6 - 1/3 = 1/x - 1/6, solving gives x = 12.

The reciprocals are 1/4, 1/2, and 1/x. The common difference is 1/2 - 1/4 = 1/4, so 1/x = 1/2 + 1/4 = 3/4, thus x = 4/3.

The complement of A in U is the set of elements in U that are not in A, which is {1, 3, 5, 7, 9, 10}.

The complement of set A consists of elements in the universal set U that are not in set A. Therefore, the complement is {1, 3, 5}.

Using the principle of inclusion-exclusion, the number of elements in either A or B is: (A + B - Both) = 40 + 30 - 10 = 60. Therefore, elements in neither = U - (A ∪ B) = 100 - 60 = 40.

Let the two angles be x and x - 10. Since they are complementary, x + (x - 10) = 90. Solving gives x = 50 degrees, and the other angle is 40 degrees.

Let the smaller angle be x. Then the larger angle is x + 10. Since they are complementary, x + (x + 10) = 90. Solving gives x = 40 degrees, so the angles are 40 and 50 degrees.

Let the smaller angle be x. Then the larger angle is 2x. The equation x + 2x = 90 gives x = 30 degrees and 2x = 60 degrees.

Complementary angles add up to 90 degrees. Therefore, the other angle is 90 - 25 = 65 degrees.

Complementary angles are defined as two angles whose measures add up to 90 degrees.

Complementary angles sum to 90 degrees, so the maximum measure of either angle can be 90 degrees.

Complementary angles sum to 90 degrees. Therefore, if one angle is 30 degrees, the other must be 90 - 30 = 60 degrees.

Angles measuring less than 90 degrees are classified as acute angles.

If two angles are equal and one measures 40 degrees, the other must also measure 40 degrees.

If two angles are equal and their sum is 180 degrees, they are straight angles, each measuring 90 degrees.

Vertically opposite angles are formed when two lines intersect and are always equal.

Vertically opposite angles are formed when two lines intersect and are always equal.

The centers of two intersecting circles are equidistant from the points of intersection.