Circumference of a circle = 2πr = 2π(4) = 8π cm.

The slopes of perpendicular lines are negative reciprocals. The negative reciprocal of 4 is -1/4.

The distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2 - x1)² + (y2 - y1)²). Here, distance = √((2 - 2)² + (7 - 3)²) = √(0 + 16) = 4.

The slope is calculated as (y2 - y1) / (x2 - x1). Here, it is (5 - 2) / (1 - 1), which is undefined.

The lengths of the sides are 4, 3, and 5 (using the Pythagorean theorem). Therefore, the perimeter = 4 + 3 + 5 = 12.

The distance between any two corresponding points on parallel lines is constant and equal to the distance between the lines, which is 5 units.

Corresponding angles are equal when two lines are parallel, so the measure of the corresponding angle is also 45 degrees.

Same-side interior angles are supplementary, so the same-side interior angle is 180 - 30 = 150 degrees.

Alternate exterior angles are equal, so the alternate exterior angle is also 40 degrees, making the other angle 140 degrees.

The corresponding interior angle is supplementary to the exterior angle, so it measures 60 degrees.

The product of the slopes of two perpendicular lines is -1.

Vertical angles are equal, so the other pair of vertical angles also measures 40 degrees.

Vertical angles are equal, so the other pair of vertical angles also measures 45 degrees.

Same-side interior angles are supplementary, so the other angle is 180 - 110 = 70 degrees.

The slope of a line perpendicular to another is the negative reciprocal. Therefore, the slope of line B is -1/3.

The slope of line A is -3. The slope of a line perpendicular to it is the negative reciprocal, which is 1/3.

The distance between two points (x1, y1) and (x2, y2) is given by the formula √((x2 - x1)² + (y2 - y1)²). Here, distance = √((2 - 2)² + (7 - 3)²) = √(0 + 16) = 4 units.

The sum of angles in a triangle is 180 degrees. Angle C = 180 - (50 + 60) = 70 degrees.

Parallel lines have the same slope. The slope is -3. Using point-slope form: y - 4 = -3(x - 1) gives y = -3x + 7.

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

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