Question

college inscribed angles
directions: solve for the missing arc or angle
1)
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2)
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3)
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4)
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5)
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6)
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7)
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8)
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Explanation:

1)

Step1: Identify inscribed angle rule

An inscribed angle is half its intercepted arc.

Step2: Calculate the angle

The intercepted arc is $80^\circ$.
$\text{Angle} = \frac{1}{2} \times 80^\circ = 40^\circ$

2)

Step1: Identify inscribed angle rule

An inscribed angle is half its intercepted arc.

Step2: Calculate the angle

The intercepted arc is $150^\circ$.
$\text{Angle} = \frac{1}{2} \times 150^\circ = 75^\circ$

3)

Step1: Identify inscribed angle rule

An inscribed angle is half its intercepted arc.

Step2: Calculate the angle

The intercepted arc is $100^\circ$.
$\text{Angle} = \frac{1}{2} \times 100^\circ = 50^\circ$

4)

Step1: Identify intercepted arc rule

The intercepted arc is twice the inscribed angle.

Step2: Calculate the arc

The inscribed angle is $83^\circ$.
$\text{Arc} = 2 \times 83^\circ = 166^\circ$

5)

Step1: Identify intercepted arc rule

The intercepted arc is twice the inscribed angle.

Step2: Calculate the arc

The inscribed angle is $37^\circ$.
$\text{Arc} = 2 \times 37^\circ = 74^\circ$

6)

Step1: Identify inscribed angle rule

An inscribed angle is half its intercepted arc.

Step2: Calculate the angle

The intercepted arc is $90^\circ$.
$\text{Angle} = \frac{1}{2} \times 90^\circ = 45^\circ$

7)

Step1: Identify intercepted arc rule

The intercepted arc is twice the inscribed angle.

Step2: Calculate the arc

The inscribed angle is $40^\circ$.
$\text{Arc} = 2 \times 40^\circ = 80^\circ$

8)

Step1: Identify inscribed angle rule

An inscribed angle is half its intercepted arc.

Step2: Calculate the angle

The intercepted arc is $60^\circ$.
$\text{Angle} = \frac{1}{2} \times 60^\circ = 30^\circ$

Answer:

1. $\boldsymbol{40^\circ}$
2. $\boldsymbol{75^\circ}$
3. $\boldsymbol{50^\circ}$
4. $\boldsymbol{166^\circ}$
5. $\boldsymbol{74^\circ}$
6. $\boldsymbol{45^\circ}$
7. $\boldsymbol{80^\circ}$
8. $\boldsymbol{30^\circ}$