Lines And Angles — Formula Sheet

Straight angle = 180°

One degree = straight angle / 180 equal parts

Complementary angles: sum = 90°

Supplementary angles: sum = 180°

Linear pair: two adjacent angles on a line add to 180°

Angle Sum Property of a Triangle: ∠A + ∠B + ∠C = 180°

Exterior Angle Theorem: ∠ACD = ∠A + ∠B

If one angle of a triangle equals the sum of the other two angles, then the triangle is a right triangle.

Angle 4 times its supplement: x = 4(180 - x) ⟹ 5x = 720 ⟹ x = 144°

The locus of a point moving under certain conditions is the path or the geometrical figure, every point of which satisfies the given condition(s).

A point moving at a constant distance d from a fixed point O traces a circle of radius d centred at O.

The locus of a point equidistant from two given points is the perpendicular bisector of the line segment joining the two points.

The locus of a point equidistant from two intersecting lines is the pair of lines bisecting the angles formed by the given lines.

The locus of a point at distance 5 cm from a given line AB is two lines parallel to AB, one on each side, at 5 cm distance.