Question

complementary and supplementary angles

1. underline the measure of each angle (use

a

b

c

d

1. find the angles that are each pair of supplementary angles

∠afb and
∠afe and
∠afd and

1. find the angles that are each pair of complementary angles.

∠afc and
∠afb and

1. angles a and b are supplementary angles. the measure of angle a is 110°. find the measure of ∠b.

a. equation:
b. m∠b

1. the measure of angle is 20° larger and forms a complementary angle. find m∠q

a. equation:
b. m∠q

1. angles f and angle g are complementary. angle f measures (3x - 2)° and angle g measures 42°. find the value of x and the measure of each angle

a. equation:

Explanation:

Step1: Read angles from protractor

• $m\angle AOB = 130^\circ$
• $m\angle AOC = 100^\circ$
• $m\angle AOD = 80^\circ$
• $m\angle AOE = 60^\circ$

Step2: Find supplementary angles (sum to $180^\circ$)

• For $\angle AOB$: $180^\circ - 130^\circ = 50^\circ$, no matching angle, so none.
• For $\angle AOD$: $180^\circ - 80^\circ = 100^\circ = m\angle AOC$, so $\angle AOC$.
• For $\angle AOE$: $180^\circ - 60^\circ = 120^\circ$, no matching angle, so none.

Step3: Find complementary angles (sum to $90^\circ$)

• For $\angle AOC$: $90^\circ - 100^\circ$ invalid, so none.
• For $\angle AOB$: $90^\circ - 130^\circ$ invalid, so none.

Step4: Solve supplementary angle pair A&B

Given $m\angle A = 105^\circ$, supplementary sum = $180^\circ$
Equation: $m\angle B = 180^\circ - 105^\circ$
Calculation: $m\angle B = 75^\circ$

Step5: Solve complementary angle pair

Given $m\angle D = 2m\angle C$, complementary sum = $90^\circ$
Equation: $2m\angle C + m\angle C = 90^\circ$
Calculation: $3m\angle C = 90^\circ \implies m\angle C = 30^\circ$, $m\angle D = 60^\circ$

Answer:

1.

• A. $130^\circ$
• B. $100^\circ$
• C. $80^\circ$
• D. $60^\circ$

2.

• $\angle AOB$ and: None
• $\angle AOD$ and: $\angle AOC$
• $\angle AOE$ and: None

3.

• $\angle AOC$ and: None
• $\angle AOB$ and: None

4.
a. Equation: $m\angle B = 180^\circ - 105^\circ$
b. $m\angle B = 75^\circ$

5.
a. Equation: $2m\angle C + m\angle C = 90^\circ$
b. $m\angle D = 60^\circ$