The angle formed by a tangent and a chord through the point of contact is equal to the angle subtended by the chord at the circumference.

The angle formed by two tangents from a point outside a circle is half the difference of the measures of the intercepted arcs.

The exterior angle is equal to the sum of the two remote interior angles. Therefore, the exterior angle measures 40 + 60 = 100 degrees.

The exterior angle is equal to the sum of the two remote interior angles. Therefore, it is 45 + 55 = 100 degrees.

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

The measure of an inscribed angle is half the measure of the intercepted arc. Therefore, it is 80 degrees / 2 = 40 degrees.

Alternate exterior angles are equal, so angle 3 is also 45 degrees.

Corresponding angles are equal when two parallel lines are cut by a transversal.

Angle A is equal to angle B because they are corresponding angles, so angle A = 70 degrees.

Exterior angles formed by a transversal with parallel lines are supplementary to the interior angles. Therefore, angle x = 180 - 40 = 140 degrees.

Exterior angles are supplementary to interior angles. Therefore, x = 180 - 120 = 60 degrees.

Corresponding angles are equal, so angle x is also 75 degrees.

The corresponding angle will measure 75 degrees, and the alternate interior angle will measure 105 degrees.

Corresponding angles are equal when two parallel lines are cut by a transversal.

In an equilateral triangle, each angle measures 60°.

The measure of each interior angle of a regular hexagon is given by (n-2) × 180/n, where n is the number of sides. For a hexagon, n = 6, so each angle is (6-2) × 180/6 = 120 degrees.

The measure of each interior angle of a regular polygon can be calculated using the formula [(n-2) × 180] / n. For a pentagon (n=5), each angle = [(5-2) × 180] / 5 = 108 degrees.

Interior angles on the same side of the transversal are supplementary. Therefore, the angle formed is 180 - 50 = 130 degrees.

According to the inscribed angle theorem, the angle subtended by a diameter at any point on the circle is always 90 degrees.

According to the inscribed angle theorem, the angle subtended by a diameter at any point on the circle is always 90 degrees.

The angle subtended by an arc at the center of a circle is twice the angle subtended at any point on the remaining part of the circle.

Arc length = rθ, where θ is in radians. Thus, 10 = 5θ, so θ = 2 radians. Converting to degrees: θ = 2 * (180/π) ≈ 114.6 degrees.

The measure of the central angle is equal to the measure of the arc it subtends, which is 120 degrees.

The formula for the arc length is L = rθ, where θ is in radians. Thus, θ = L/r = 5/10 = 0.5 radians. Converting to degrees, θ = 0.5 * (180/π) ≈ 28.65 degrees, which is closest to 30 degrees.

Corresponding angles are equal when two parallel lines are cut by a transversal.

Corresponding angles are equal when two parallel lines are cut by a transversal.

Corresponding angles are equal, so the measure is also 45 degrees.

Corresponding angles are equal when a transversal intersects two parallel lines.

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

Sorted data: 1, 2, 3, 4; Median = (2 + 3) / 2 = 2.5.