**What is the relationship between an inscribed angle and its intercepted arc? Theorem 70: The measure of an inscribed angle in a circle equals half the measure of its intercepted arc.**

**What is the relationship between an inscribed angle and the arc it intercepts?** Inscribed Angle Theorem:

The measure of an inscribed angle is half the measure of the intercepted arc. That is, m∠ABC=12m∠AOC. This leads to the corollary that in a circle any two inscribed angles with the same intercepted arcs are congruent.

**What seems to be the relationship between an inscribed angle and its intercepted arc How about central angle and inscribed angle?** The measure of the inscribed angle is half the measure of the arc it intercepts. If a central angle and an inscribed angle intercept the same arc, then the central angle is double the inscribed angle, and the inscribed angle is half the central angle.

**What is the intercepted arc of an inscribed angle?** Inscribed angles are angles whose vertices are on a circle and that intersect an arc on the circle. The measure of an inscribed angle is half of the measure of the intercepted arc and half the measure of the central angle intersecting the same arc. Inscribed angles that intercept the same arc are congruent.

## What is the relationship between an inscribed angle and its intercepted arc? – Related Questions

### What have you observed with the measure of the inscribed angle and its intercepted arc?

If an angle is an inscribed angle, then its measure is equal to half the measure of the intercepted arc. If an angle is an inscribed angle, then its measure is equal to half the measure of the intercepted arc.

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

The arc measure equals the corresponding central angle measure, in radians. That’s why radians are natural: a central angle of one radian will span an arc exactly one radius long.

### Why are inscribed angles half the arc?

The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle. Therefore, the angle does not change as its vertex is moved to different positions on the circle.

### What is the measure of XYZ?

Answer Expert Verified Angle subtended by an arc at the centre is twice of the angle subtended at any point on the circle . And in the given diagram, angle subtended on the circle by arc XZ=60 degree . So arc XZ =2*60=120.

### What conjecture can you draw from the measures of inscribed angle and its intercepted arc?

Corollary (Inscribed Angles Conjecture II ): In a circle, two inscribed angles with the same intercepted arc are congruent. Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure.

### How did you identify and name the angles and its intercepted arcs?

Answer Expert Verified

To find an angle is to look for a point in which two lines intersect. And to name that angle; line A intersects line B at point C, so the angle will be named

Step-by-step explanation:

If the Inscribed Angle is 35 degree, It’s Intercepted Arc is equal to 70 degree.

### What is 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 an intercepted arc length?

The length of the intercepted arc is equal to the circumference of the circle. Therefore, the radian measure of this central angle is the circumference of the circle divided by the circle’s radius, .

### What is a major arc?

A major arc is the longer arc connecting two endpoints on a circle. The measure of a major arc is greater than 180° , and equal to 360° minus the measure of the minor arc with the same endpoints. An arc measuring exactly 180° is called a semicircle .

### What is the relation between angle arc and radius?

Clearly, that ratio is independent of r. In general, the radian measure of an angle is the ratio of the arc length cut off by the corresponding central angle in a circle to the radius of the circle, independent of the radius. θ = arc lengthradius .

### What is the longest chord?

Hence, Diameter is the longest chord.

### Is the central angle the same as the arc?

Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one (measured in radians). The central angle is also known as the arc’s angular distance.

### Is the inscribed angle the same as the arc?

An inscribed angle is an angle with its vertex on the circle and whose sides are chords. The intercepted arc is the arc that is inside the inscribed angle and whose endpoints are on the angle.

### What angle is XYZ?

In any isosceles triangle, the measure of two angles are equal. In this case, angle is equal to angle . Angles on a straight line sum to 180 degrees. This means that we can calculate the measure of angle by subtracting 122 from 180.

### What is the measure of overline XYZ 82?

In triangle XYZ the measure of angle XYZ is 82 ° and the measure of angle YXZ ‘is 58 ° .

### What is the measure of XYZ 68?

What is the measure of angle XYZ 68? Answer: Option B 34° is the answer.

### What are the intercepted arcs of CFD?

What are the intercepted arcs of CFD? 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.

### Does a semi circle have two right angles?

Yes. The semi-circle can even be referred to sometimes as a ( Curvilinear) Diangle, sum of the two shown right angles is π. If Q and P are opposite points of a diameter in a circle then the tangent at Q makes a right angle to the line PQ.

### What is inscribed angle and example?

An inscribed angle has one endpoint on the edge of the circle and then cuts across the rest of the circle. The vertex of its angle is on the circumference. If the inscribed angle measure x, the central angle will measure 2x. For example, if the central angle is 90 degrees, the inscribed angle is 45 degrees.

### What is the relationship between central and inscribed angles?

Central angle = Angle subtended by an arc of the circle from the center of the circle. Inscribed angle = Angle subtended by an arc of the circle from any point on the circumference of the circle. Also called circumferential angle and peripheral angle. if and only if both angles intercepted the same arc.