Vertical, Complementary, and Supplementary Angles Unit 1 Part 5

Vertical angles are congruent. A B C D ∠ A is congruent to ∠ B ∠ C is congruent to ∠ D Opposite angles

Complementary angles Two adjacent angles whose sum equals 90 degrees. A B C D ∠ ACB + ∠ BCD = 90 degrees

Complementary angles

Supplementary angles Two adjacent angles whose sum equals 180 degrees. G K L M ∠ KLG + ∠ GLM = 180 degrees

Supplementary angles

Problems If angle A is x + 10 and angle B is 4x – 35 then what is the value of x and the measure of angle A ? A B C D

Solution X + 10 = 4x – x = 4x – 45 -4x -3x = x = 15, m ∠ A = 25 A B C D

Problems Angle ABD and angle DBC are complementary angles (equals 90 degrees). If m ∠ ABD = (3x – 1)° and m ∠ DBC = (2x + 6)° what is the measure of m ∠ ABD. A D B C

Solution ∠ ABD + ∠ DBC = 90 2x x – 1 = 90 5x + 5 = 90 (gather) (separate) 5x = 85 X= 17 2(17) + 6 = 40 degrees  m ∠ ABD A D B C

Problems ∠ A and ∠ B are supplementary angles. ( equals 180 degrees) If m ∠ A = 75 degrees how much is angle B ? m ∠ A + m ∠ B = ∠ B = m ∠ B = 105 degrees