# What is the measure of the arc intercepted?

## What is the measure of the arc intercepted?

An especially interesting result of the Inscribed Angle Theorem is that an angle inscribed in a semi-circle is a right angle. In a semi-circle, the intercepted arc measures 180 ° and therefore any corresponding inscribed angle would measure half of it.

### When the measure of the intercepted arc is 180?

An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two. Every pair of endpoints on a circle either defines one minor arc and one major arc, or two semicircles.

#### What does it mean when an arc is intercepted?

An intercepted arc can therefore be defined as an arc formed when one or two different chords or line segments cut across a circle and meet at a common point called a vertex.

What is the measure of the inscribed angle whose intercepted arc is 120 degrees?

The inscribed angles create three intercepted arcs. We can determine the measurement of the arcs by dividing 360 (the measure of the circle) by 3 (the number of arcs). Each arc measures 120 degrees. Therefore, the inscribed angle associated with it is 1/2 of 120 degrees or 60 degrees.

Which circle shows an intercepted arc?

The intercepted arc is a section of the circumference of a circle. It is encased on either side by two different chords or line segments that meet at one point, called a vertex, on the other side of the circle or in the middle of the circle.

## What is the relationship between the inscribed angle and the intercepted arc?

The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Inscribed angles that intercept the same arc are congruent.

### What seems to be the relationship between an inscribed angle and its intercepted arc?

#### What can you say about the measure of the central angle and its intercepted arc?

The measure of a central angle is equal to the measure of its intercepted arc. A chord is a segment that has is endpoints on a circle. A line is called a straight angle and it forms a 180 degree angle. A central angle is an angle with its vertex at the center of a circle and its sides are radii of the same circle.

What is the relationship between a central angle and its intercepted arc?

Central Angles and Intercepted Arcs – Concept A central angle is an angle whose vertex is on the center of the circle and whose endpoints are on the circle. The angle measure of the central angle is congruent to the measure of the intercepted arc which is an important fact when finding missing arcs or central angles.

What is the measure of an inscribed angle whose intercepted arc measures 126?

2. SOLUTION: If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc. Therefore, ANSWER: 126 3.

## How to find the measure of an intercepted arc?

Solution: Show that central angles = arcs they intercept. Examples to show how to use the property that the measure of a central angle is equal to the measure of its intercepted arc to find the missing measures of arcs and angles in given figures. If playback doesn’t begin shortly, try restarting your device.

### How is the central angle related to the intercepted arc?

The endpoints on the circle are also the endpoints for the angle’s intercepted arc. The angle measure of the central angle is congruent to the measure of the intercepted arc which is an important fact when finding missing arcs or central angles.

#### How do you find the intercepted arc of a chord?

For intersecting chords, the intercepted arc is given by, The inscribed angle = half the sum of intercepted arcs. External inscribed angle: The size of the vertex angle outside the circle = 1/2 × (difference of intercepted arcs) Worked out examples about the intercepted arc. Find angle ABC in the circle shown below.

What is the relationship between inscribed angles and their arcs?

What is the relationship between inscribed angles and their arcs? The measure of an inscribed angle is half the measure the intercepted arc. The formula is: Measure of inscribed angle = 1/2 × measure of intercepted arc. Example: Find the value of x. Solution: x = m∠AOB = 1/2 × 120° = 60° Angle with vertex on the circle (Inscribed angle)