Practice worksheet on central and inscribed angles in circles, including problems for identifying and calculating angle measures.

Since I can't view or access images directly, I can’t see the specific diagram or details of the problems in your uploaded image. However, based on the text you've provided, I can help you solve the Central Angles and Inscribed Angles practice problems step by step.

Let’s go through each problem logically, assuming standard circle geometry rules:

---

Key Concepts:

1. Central Angle: An angle whose vertex is at the center of the circle.
- The measure of a central angle is equal to the measure of its intercepted arc.

2. Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords.
- The measure of an inscribed angle is half the measure of its intercepted arc.

3. Arc Measure: The measure of an arc is equal to the measure of its central angle.

4. Inscribed Angle Theorem:
$$
\text{Inscribed Angle} = \frac{1}{2} \times \text{Intercepted Arc}
$$

5. Opposite Angles in a Cyclic Quadrilateral:
- Sum of opposite angles = 180°

6. Angle formed by two chords intersecting inside a circle:
$$
\text{Angle} = \frac{1}{2}(\text{Arc}_1 + \text{Arc}_2)
$$

7. Tangent-Chord Angle:
$$
\text{Angle} = \frac{1}{2} \times \text{Intercepted Arc}
$$

---

Now let's work through the problems as listed:

---

Problems 1–3: Refer to the figure (assume a circle with center O, points A, B, C on the circle)

> 1. Name the chord(s)
A chord is a line segment with both endpoints on the circle.
So possible chords: AB, BC, AC, etc., depending on the figure.
Assuming triangle ABC is inscribed:
✔ Chords: AB, BC, AC

> 2. Name the central angle(s)
A central angle has its vertex at the center O.
If ∠AOB, ∠BOC, ∠AOC are shown:
✔ Central angles: ∠AOB, ∠BOC, ∠AOC

> 3. Name the inscribed angle(s)
An inscribed angle has its vertex on the circle.
For example, if ∠ABC, ∠BAC, ∠ACB are shown:
✔ Inscribed angles: ∠ABC, ∠BAC, ∠ACB

---

Problems 4–7: Find indicated measures

#### 4.
Given: A circle with center O, and points labeled such that:
- m∠COA = ? (central angle)
- m∠CD = ? (arc CD)

But from the notation:
- m∠COA → central angle
- mCD → arc CD

If ∠COA intercepts arc CA, then:
$$
m\angle COA = m\widehat{CA}
$$

But we need more info. Let’s assume typical setup: If arc CD is given or implied...

Wait — perhaps it's like this:

Suppose there is a central angle ∠COA, and we're asked for:
- m∠COA = ?
- m∠CD = ?

Possibly typo? Maybe meant:
- m∠COA = ?
- m$\widehat{CD}$ = ?

Let’s suppose the diagram shows:
- Point D on the circle
- ∠COD is central angle → so m∠COD = m$\widehat{CD}$

But without values, we need numbers.

Wait — perhaps the diagram includes angles or arcs with measures.

Alternatively, maybe the image shows a circle divided into parts.

Let’s suppose a common problem type:

> Example: In a circle, arc AB = 60°, what is the central angle ∠AOB?

Then:
$$
m\angle AOB = m\widehat{AB} = 60^\circ
$$

And if inscribed angle ∠ACB intercepts arc AB, then:
$$
m\angle ACB = \frac{1}{2} \times 60^\circ = 30^\circ
$$

But since no numbers are given in your text, perhaps the image had labeled arcs or angles.

Let’s move to next section.

---

Find the unknown value (problems 6–9)

> 6. Given a circle with central angle and arc, find x.

Common type: Two arcs or angles given, solve for x.

Example: Suppose arc AB = 2x, arc BC = 3x, and total circle = 360°, so:
$$
2x + 3x = 360^\circ \Rightarrow 5x = 360 \Rightarrow x = 72^\circ
$$

But again, no numbers in text.

---

> 7. m∠CED = ?
Assume E is on the circle, C and D are points.

If ∠CED is an inscribed angle intercepting arc CD, then:
$$
m\angle CED = \frac{1}{2} m\widehat{CD}
$$

But need arc measure.

Similarly,

> 8. m∠GH = ? → probably typo; should be m∠GCH or something.

Likely: m∠GCH = ? where G and H are on circle.

Again, depends on intercepted arc.

---

Problem 10–12: Passenger airplane flight path around circular radar screen

> "The figure shows a passenger airplane's flight path on a circular radar screen as an arc that is tangent to the tower."

So: Airplane flies along a tangent line to a circle (radar screen), touching at point T.

Tower is at center O.

Let’s suppose:

- Tangent touches circle at point T
- Airplane approaches along tangent line
- Points M, N, K, etc., labeled

Typical problem:

> 10. What is m∠K?

Assume ∠K is formed between tangent and chord.

There’s a theorem:
> The angle between a tangent and a chord is equal to the inscribed angle on the opposite side of the chord.

So:
$$
\angle \text{between tangent and chord} = \frac{1}{2} \times \text{intercepted arc}
$$

Suppose:
- Tangent at T
- Chord TK
- Then ∠K = angle between tangent and chord TK

Then:
$$
m\angle K = \frac{1}{2} m\widehat{TK}
$$

But without values, hard to compute.

---

> 11. What is m∠KMT?

If M is on the circle, and K and T are points, then ∠KMT is an inscribed angle.

Suppose it intercepts arc KT.

Then:
$$
m\angle KMT = \frac{1}{2} m\widehat{KT}
$$

> 12. What is m∠KMT? — same as above? Possibly typo.

Maybe different angle.

Wait — perhaps:
- K is point of tangency
- M is another point
- ∠KMT is formed by tangent and chord

But again, need diagram.

---

How to Solve These Without Image?

Since I can’t see the image, here’s how you can solve them:

#### Step-by-step approach:

1. Identify the type of angle:
- Is it central? → equals arc measure
- Is it inscribed? → half the arc
- Is it formed by tangent and chord? → half the intercepted arc
- Do two chords intersect? → half the sum of intercepted arcs

2. Label known arcs or angles from the diagram.

3. Use circle theorems:
- Inscribed angle = ½ arc
- Central angle = arc
- Tangent-chord angle = ½ arc
- Opposite angles in cyclic quadrilateral = 180°

4. Set up equations if variables are involved.

---

Example Problem (Hypothetical):

Suppose in problem 4:
- Central angle ∠COA = 80°
- Then m$\widehat{CA}$ = 80°
- If ∠CBA is inscribed angle intercepting arc CA, then:
$$
m\angle CBA = \frac{1}{2} \times 80^\circ = 40^\circ
$$

---

Final Advice:

Please provide:
- The measures shown in the diagram (e.g., “arc AB = 60°”, “angle at center = 100°”)
- Or describe the figure: e.g., “a circle with center O, points A, B, C on circumference, triangle ABC inscribed”

Then I can give exact answers.

Alternatively, if you can type out the values from the image (like arc measures, angles, labels), I can solve all problems.

Let me know!