Perpendicular lines intersect at right angles, which measure 90 degrees.

Vertically opposite angles are equal. Therefore, the measure of the vertically opposite angle is also 70 degrees.

Vertically opposite angles are equal. Therefore, the measure of the vertically opposite angle is also 35 degrees.

Adjacent angles formed by intersecting lines are supplementary. Therefore, 180 - 70 = 110 degrees.

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

Area of sector = (θ/360) × πr² = (90/360) × π × 10² = (1/4) × 100π = 25π cm².

Area of sector = (θ/360) × πr² = (90/360) × π × 6² = (1/4) × 36π = 9π cm².

Area of sector = (θ/360) × πr² = (90/360) × π(6)² = (1/4) × 36π = 9π cm².

Area = side² = 8² = 64 cm²

Area = 1/2 * (base1 + base2) * height = 1/2 * (5 + 7) * 4 = 24 cm²

Area = (√3/4) * side² = (√3/4) * 6² = (√3/4) * 36 = 9√3 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=2, k=-3, r=4. Thus, (x-2)² + (y+3)² = 16.

The standard equation of a circle is (x-h)² + (y-k)² = r². Here, h=3, k=-2, r=4. Thus, (x-3)² + (y+2)² = 16.

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.

Arc length = (θ/360) × 2πr = (60/360) × 2π(7) = (1/6) × 14π = 7π/3 cm.

Arc length = (θ/360) × 2πr = (60/360) × 2π(5) = (1/6) × 10π = 5π/6 cm.

Using Heron's formula, the area is 30 cm². The altitude = (2 * Area) / base = (2 * 30) / 13 = 6 cm.

In a right triangle, the altitude from the right angle to the hypotenuse is equal to the length of the other side. Thus, the altitude is 6 cm.

Diagonal = √(length² + width²) = √(3² + 4²) = √(9 + 16) = √25 = 5 cm

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.

Using the median formula: m_a = 1/2 * sqrt(2b^2 + 2c^2 - a^2), where a = BC, b = AC, c = AB. m_a = 1/2 * sqrt(2*6^2 + 2*10^2 - 8^2) = 7 cm.

Supplementary angles sum to 180 degrees. Therefore, the angle is 180 - 75 = 105 degrees.

Supplementary angles sum up to 180 degrees. Therefore, the angle measures 180 - 110 = 70 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.

Complementary angles sum up to 90 degrees. If one angle is 30 degrees, the other angle is 90 - 30 = 60 degrees.

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.