Supplementary angles do not need to be adjacent (Figure 8).įigure 8 Nonadjacent supplementary angles.īecause m ∠8 + m ∠9 = 180°, ∠8 and ∠9 are supplementary. SOLUTION: The angles 9 and 10 are supplementary or form a. Theorem 9: If two adjacent angles have their noncommon sides lying on a line, then they are supplementary angles. Find the measure of each numbered angle and name the theorems used that justify your work. Therefore m ∠6 + m ∠7 = 180°, so ∠6 and ∠7 are supplementary. Supplementary angles are two angles whose sum is 180°. Theorem 8 now tells you that m ∠ A = m ∠ C.įigure 5 Two angles complementary to the same angleįigure 6 Two angles complementary to equal angles Also, ∠ C and ∠ D are complementary, and m ∠ B = m ∠ D. In Figure 6, ∠ A and ∠ B are complementary. In Figure 5, ∠ A and ∠ B are complementary. Theorem 8: If two angles are complementary to the same angle, or to equal angles, then they are equal to each other. In Figure 4, because m ∠3 + m ∠4 = 90°, ∠3, and ∠4, are complementary.įigure 4 Nonadjacent complementary anglesĮxample 1: If ∠5 and ∠6 are complementary, and m ∠5 = 15°, find m ∠6. In Figure 3, because ∠ ABC is a right angle, m ∠1 + m ∠2 = 90°, so ∠1 and ∠2 are complementary.Ĭomplementary angles do not need to be adjacent.

Theorem 7: Vertical angles are equal in measure.Ĭomplementary angles are any two angles whose sum is 90°. In Figure 2, line l and line m intersect at point Q, forming ∠1, ∠2, ∠3, and ∠4.įigure 2 Two pairs of vertical angles and four pairs of adjacent angles. Any two of these angles that are not adjacent angles are called vertical angles. Vertical angles are formed when two lines intersect and form four angles. In Figure 1, ∠1 and ∠2 are adjacent angles. Summary of Coordinate Geometry FormulasĬertain angle pairs are given special names based on their relative position to one another or based on the sum of their respective measures.Īdjacent angles are any two angles that share a common side separating the two angles and that share a common vertex.Slopes: Parallel and Perpendicular Lines.Similar Triangles: Perimeters and Areas.Proportional Parts of Similar Triangles.Formulas: Perimeter, Circumference, Area.Proving that Figures Are Parallelograms.Triangle Inequalities: Sides and Angles.Special Features of Isosceles Triangles.Classifying Triangles by Sides or Angles.Lines: Intersecting, Perpendicular, Parallel.

Supplementary angle theorem