Supplementary angles sum up to 180 degrees. Therefore, the other angle = 180 - 120 = 60 degrees.

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

The maximum radius of each circle can be half the distance between the centers, which is 10 cm.

Vertically opposite angles are equal. Therefore, the vertically opposite angle is also 40 degrees.

If the corresponding angles are equal, it indicates that the two lines are parallel.

If the sum of the interior angles on the same side of the transversal is greater than 180 degrees, the two lines must intersect.

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

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

The angles formed by intersecting lines are supplementary. Therefore, 120 + x = 180, which gives x = 60 degrees.

The angles formed by intersecting lines are supplementary. Therefore, x = 180 - 40 = 140 degrees.

Vertically opposite angles are equal. Therefore, the vertically opposite angle is also 120 degrees.

Adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180 degrees. Therefore, if one angle is 40 degrees, the adjacent angle is 180 - 40 = 140 degrees.

Vertically opposite angles are equal when two lines intersect. Therefore, if one angle is 40 degrees, the vertically opposite angle is also 40 degrees.

Let the angles be 2x and 3x. Since they are supplementary, 2x + 3x = 180 degrees. Thus, 5x = 180 degrees, x = 36 degrees. The larger angle is 3x = 108 degrees.

Adjacent angles formed by intersecting lines are supplementary. Therefore, 30 + x = 180, which gives x = 150 degrees.

When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, but the angles formed by the intersecting lines sum up to 180 degrees.

When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, and since there are two pairs of vertically opposite angles, the sum of the angles formed at the intersection is 180 degrees.

Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, the other alternate interior angle is also 75 degrees.

Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, the other angle is also 45 degrees.

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

A × B = |i  j  k|\n|2  3  1|\n|1 -2  4| = (3*4 - 1*(-2))i - (2*4 - 1*1)j + (2*(-2) - 3*1)k = 10i - 5j - 7k.

R = A + B = (2 - 1)i + (3 + 4)j = 1i + 7j.

cos(θ) = (A · B) / (|A| |B|) = (2*3 + 3*4) / (√(2^2 + 3^2) * √(3^2 + 4^2)) = 0.6, θ = 53.13 degrees.

cos(θ) = (A · B) / (|A||B|) = (8 + 15) / (√(13) * √(41)). θ = 60 degrees.

cos(θ) = (A · B) / (|A||B|) = (2*4 + 3*5) / (√(2^2 + 3^2) * √(4^2 + 5^2)) = 0.5, θ = 60 degrees.

Vectors A and B are parallel because B = 2A.

cos(θ) = (A · B) / (|A| |B|). A · B = 8 + 0 + 3(0) = 8; |A| = √(2^2 + 3^2) = √13; |B| = √(4^2 + 1^2) = √17. θ = cos^(-1)(8/(√13 * √17)).

A · B = (3)(2) + (4)(-1) = 6 - 4 = 2.

A × B = |i  j  k| |3  4  0| |4  3  0| = (0 - 0)i - (0 - 0)j + (9 - 12)k = -3k.

cos(θ) = (A · B) / (|A||B|) = (4*-3 + 3*4) / (5*5) = 0, θ = 90 degrees.