Vertical , Complementary, and Supplementary Angles

Unit 1 Part 5

Vertical angles are congruent.

A BC

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

CD

∠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 BC

D

Solution

X + 10 = 4x – 35

- 10 - 10

x = 4x – 45

-4x -4x

-3x = -45

-3 -3

x = 15 , m ∠ A = 25

A BC

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 + 6 + 3x – 1 = 90

5x + 5 = 90 (gather)

-5 -5 (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 = 180∠ ∠ 75 + B = 180∠-75 -75

m B = 105 degrees∠