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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∠