Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Inscribed Angles Practice Quiz

Improve Your Skills with Central and Inscribed Angles

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art illustrating a trivia quiz about Circle Angle Challenge for high school geometry students.

In a circle, an inscribed angle intercepts an arc. What is the relationship between the measure of the inscribed angle and its intercepted arc?
The inscribed angle measures half of its intercepted arc
The inscribed angle is twice the intercepted arc
There is no fixed relationship
The inscribed angle equals the measure of its intercepted arc
According to the Inscribed Angle Theorem, the measure of an inscribed angle is exactly half the measure of its intercepted arc. This fundamental property applies to all inscribed angles in a circle.
What is the measure of a central angle compared to its intercepted arc?
It is half the measure of its intercepted arc
It is double the measure of its intercepted arc
It is equal to the measure of its intercepted arc
It is always 90° regardless of the arc
A central angle is formed by two radii, which makes its measure identical to the measure of the intercepted arc. This direct relationship is one of the basic properties of circles.
Which option best defines an intercepted arc in a circle?
The entire circumference of the circle
The shorter arc connecting two points on a circle
The portion of the circle's circumference between the two points where an angle's sides intersect the circle
The arc that is complementary to an angle
An intercepted arc is defined as the portion of the circle's circumference that lies between the two points where the sides of an angle (inscribed or central) intersect the circle. This definition is central to applying the Inscribed Angle Theorem.
If an inscribed angle intercepts an arc measuring 100°, what is the measure of the inscribed angle?
150°
100°
50°
200°
By the Inscribed Angle Theorem, an inscribed angle is half the measure of its intercepted arc. Therefore, if the intercepted arc is 100°, the inscribed angle measures 50°.
An angle inscribed in a semicircle always forms which type of angle?
Acute angle
Reflex angle
Right angle
Obtuse angle
This is a direct consequence of Thales' Theorem, which states that an angle inscribed in a semicircle is a right angle. This property is commonly used in problems involving circles.
If two inscribed angles intercept the same arc, what is true about their measures?
They are equal
They are complementary
They are supplementary
One is twice the other
According to the Inscribed Angle Theorem, all inscribed angles that intercept the same arc have equal measures. This ensures consistency in circle geometry.
An inscribed angle intercepting an arc of 80° has how many degrees?
60°
20°
80°
40°
Since an inscribed angle measures half the intercepted arc, an intercepted arc of 80° will result in an inscribed angle of 40°.
What is the measure of a central angle that intercepts an arc of 150°?
100°
75°
180°
150°
A central angle in a circle is equal in measure to its intercepted arc. Hence, if the intercepted arc is 150°, the central angle is also 150°.
An inscribed angle measuring 30° intercepts an arc of what measure?
15°
30°
60°
90°
By the Inscribed Angle Theorem, the inscribed angle is half the measure of its intercepted arc. Therefore, an angle of 30° intercepts an arc of 60°.
Two chords intersect inside a circle. If one intercepted arc measures 70° and the other intercepted arc measures 110°, what is the measure of the angle formed at the intersection?
90°
110°
80°
70°
When two chords intersect inside a circle, the measure of the angle formed is half the sum of the measures of the intercepted arcs. Hence, 1/2*(70° + 110°) equals 90°.
What is the measure of the angle formed by a tangent and a chord if the intercepted arc measures 100°?
100°
50°
75°
25°
The tangent-chord angle theorem states that the angle between a tangent and a chord is half the measure of its intercepted arc. Thus, if the intercepted arc is 100°, the angle measures 50°.
If an inscribed angle intercepts a diameter, what type of triangle is formed by the chord and the diameter?
Isosceles triangle
Right triangle
Equilateral triangle
Obtuse triangle
According to Thales' Theorem, an inscribed angle intercepting a diameter is a right angle, which forms a right triangle. This is a key concept in circle geometry.
An angle formed by two intersecting chords intercepts arcs measuring 80° and 140°. What is the measure of this angle?
90°
120°
110°
100°
The measure of an angle formed by two intersecting chords is half the sum of the intercepted arcs. In this case, 1/2*(80° + 140°) equals 110°.
If an inscribed angle and a central angle intercept the same arc, how do their measures compare?
The inscribed angle equals the central angle
They are supplementary
The inscribed angle is twice the central angle
The inscribed angle is half the measure of the central angle
By definition, the inscribed angle is half the measure of its intercepted arc while the central angle is equal to the intercepted arc. Therefore, the inscribed angle is half that of the central angle.
Which theorem explains that an angle inscribed in a semicircle is a right angle?
Cyclic Quadrilateral Theorem
Inscribed Angle Theorem
Thales' Theorem
Central Angle Theorem
Thales' Theorem states that if an angle is inscribed in a semicircle, then it is a right angle. This theorem is a cornerstone concept in circle geometry.
A tangent and a chord form an angle measuring 35° in a circle. If the intercepted arc is represented by 2x + 10 degrees, what is the value of x?
30
20
40
25
The tangent-chord angle is half the intercepted arc measure. Setting up the equation 35 = 1/2*(2x + 10) and solving for x yields x = 30.
An inscribed angle in a circle is represented as (3x + 2)° and its intercepted arc is represented as (4x + 10)°. Using the inscribed angle theorem, what is the value of x?
4
3
2
5
The inscribed angle theorem states that the inscribed angle is half the measure of its intercepted arc. Setting up the equation 3x + 2 = 1/2*(4x + 10) and solving, we find x = 3.
A cyclic quadrilateral has a pair of opposite angles expressed as (2x + 10)° and (3x - 20)°. Given that opposite angles in a cyclic quadrilateral are supplementary, what is the value of x?
38
30
36
40
In a cyclic quadrilateral, opposite angles sum to 180°. Setting up the equation (2x + 10) + (3x - 20) = 180 and solving for x gives x = 38.
Two inscribed angles intercept arcs that together measure 150°. If one inscribed angle measures 40°, what is the measure of the other inscribed angle?
45°
40°
35°
55°
An inscribed angle is half the measure of its intercepted arc. The intercepted arc corresponding to the 40° angle is 80°, so the remaining intercepted arc is 150° - 80° = 70°. The other inscribed angle is half of 70°, which is 35°.
A circle has an inscribed angle represented as (x + 20)° and its intercepted arc given by (3x + 10)°. Using the inscribed angle theorem, determine the value of x.
20
25
35
30
The inscribed angle theorem tells us that the inscribed angle is half the measure of its intercepted arc. Setting up the equation x + 20 = 1/2*(3x + 10) and solving for x yields x = 30.
0
{"name":"In a circle, an inscribed angle intercepts an arc. What is the relationship between the measure of the inscribed angle and its intercepted arc?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"In a circle, an inscribed angle intercepts an arc. What is the relationship between the measure of the inscribed angle and its intercepted arc?, What is the measure of a central angle compared to its intercepted arc?, Which option best defines an intercepted arc in a circle?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Analyze the relationship between inscribed angles and their intercepted arcs.
  2. Apply circle theorems to determine unknown angle measures.
  3. Evaluate and solve problems involving circle angle configurations.
  4. Synthesize different geometric properties to deduce angle relationships.
  5. Interpret and explain the significance of inscribed angle properties in circle geometry.

Central & Inscribed Angles Practice Test Cheat Sheet

  1. Inscribed Angle - When two chords meet on the circle's edge, they form an inscribed angle and span an intercepted arc. Mastering this concept is like unlocking the first level of circle puzzles - get it right, and the rest falls into place! Math Bits Notebook
  2. Inscribed Angle Theorem - This golden rule tells you an inscribed angle is always half the measure of its intercepted arc. Spot an 80° arc, and voilà - you've got a 40° angle waiting to be used! GeeksforGeeks
  3. Angles Subtending the Same Arc - Angles that gaze at the same arc are geometry twins - they share identical measures. Recognizing these angle pals helps you solve circle riddles faster than you can say "congruent!" Math Bits Notebook
  4. Angle in a Semicircle - An inscribed angle spanning a diameter is always a perfect right angle (90°). This neat trick transforms any semicircle into your personal right”angle generator! Math Bits Notebook
  5. Cyclic Quadrilateral Opposites - In a four”sided figure inscribed in a circle, opposite angles are best friends - they add up to 180°. Pair them wisely and watch your angle problems crumble! Math Bits Notebook
  6. Central Angle Theorem - The central angle is twice any inscribed angle that subtends the same arc. It's like applying a "double”up" rule to crack circle problems in one swift move! Cuemath
  7. Tangent‑Chord Angle - When a tangent meets a chord at the circle, that angle equals the inscribed angle on the opposite side. Known as the Alternate Segment Theorem, it's a magician's trick in geometry! Online Math Learning
  8. Exterior Angle of a Cyclic Quadrilateral - An exterior angle of a cyclic quadrilateral matches its opposite interior angle. Perfect for plugging into proofs and watching the rest of the figure fall into place! Math Bits Notebook
  9. Perpendicular Bisector of a Chord - A radius or diameter perpendicular to a chord splits both the chord and its arc into equal halves. This bisector move is your secret weapon for dividing and conquering chord challenges! Online Math Learning
  10. Equal Tangents from an External Point - Tangents drawn from the same external spot to a circle are always equal in length. Use this handy property to tackle tangent”length problems with confidence! Online Math Learning
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker