Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2. Therefore, triangle ABC is a right triangle.

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.

Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, if one angle is 65 degrees, the other alternate interior angle is also 65 degrees.

Area = πr² = 3.14 * (4)² = 3.14 * 16 = 50.24 cm²

Circumference = 2 * π * radius = 2 * π * 7 = 14π cm

The standard form of a circle's equation is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=5, so (x-3)² + (y+2)² = 25.

Diagonal = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm

Area = πr². Given area = 50π, r² = 50, r = √50 = 5√2. Diameter = 2r = 10√2 units.

The measure of each interior angle in a regular hexagon can be calculated using the formula (n-2) * 180/n, where n is the number of sides. For a hexagon, n=6, so the measure is (6-2) * 180/6 = 120 degrees.

A regular quadrilateral is a square, and each angle in a square measures 90 degrees.

The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Therefore, the exterior angle = 50 + 60 = 110 degrees.

The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Therefore, the exterior angle = 50 + 60 = 110 degrees.

In an equilateral triangle, all three angles are equal and measure 60 degrees each.

When two parallel lines are cut by a transversal, the corresponding angles are equal.

The sum of the interior angles of a triangle is 180 degrees, and the angles formed by a transversal cutting through two parallel lines are supplementary, meaning they add up to 180 degrees.

Sum of interior angles = (n-2) * 180° = (6-2) * 180° = 720 degrees