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Quizzes > High School Quizzes > Mathematics

Inscribed Angles Practice Quiz

Master inscribed angles through targeted practice problems

Difficulty: Moderate
Grade: Grade 9
Study OutcomesCheat Sheet
Paper art promoting The Inscribed Angle Challenge quiz for high school geometry students.

Which of the following best defines an inscribed angle?
An angle formed by two chords of a circle with its vertex on the circle.
An angle formed by a chord and a tangent.
An angle with its vertex at the center of the circle.
An angle outside a circle formed by two external points.
An inscribed angle is defined as an angle formed by two chords of a circle with the vertex lying on the circle. This definition distinguishes it from central angles and other angles associated with circles.
How is the measure of an inscribed angle related to its intercepted arc?
It is one-fourth of the intercepted arc.
It is equal to the intercepted arc.
It is twice the intercepted arc.
It is half the measure of the intercepted arc.
The inscribed angle theorem states that an inscribed angle is always half the measure of its intercepted arc. This fundamental relationship is key to solving many circle geometry problems.
If an inscribed angle intercepts an arc of 80°, what is the measure of the inscribed angle?
20°
40°
80°
160°
Since an inscribed angle measures half of its intercepted arc, an 80° arc results in an angle of 40°. This simple calculation is a cornerstone of circle geometry.
What is the relationship between an inscribed angle and a central angle intercepting the same arc?
The inscribed angle is twice the measure of the central angle.
They have the same measure.
The inscribed angle is half the measure of the central angle.
The inscribed angle is the supplement of the central angle.
A central angle has a measure equal to the intercepted arc while an inscribed angle is half that measure. Thus, the inscribed angle is half the measure of the central angle intercepting the same arc.
What do inscribed angles that intercept the same arc have in common?
They add up to 90°.
They are congruent.
They have different measures.
They are supplementary.
Inscribed angles intercepting the same arc are congruent, meaning they have equal measures. This property is a direct result of the inscribed angle theorem and is useful in many geometric proofs.
An inscribed angle intercepts an arc measuring 140°. What is the measure of the inscribed angle?
280°
70°
35°
140°
The inscribed angle is half of the intercepted arc. Dividing 140° by 2 gives 70°, which is the correct measure according to the inscribed angle theorem.
Two inscribed angles intercept the same arc which measures 100°. What are their measures?
They are supplementary.
One measures 30° and the other 70°.
Both measure 50°.
Both measure 100°.
Since each inscribed angle is half of the intercepted arc, both angles intercepting a 100° arc measure 50°. This demonstrates the congruence property inherent to inscribed angles intercepting the same arc.
In a circle, if an inscribed angle measures 30°, what is the measure of its intercepted arc?
90°
60°
120°
30°
The intercepted arc is twice the inscribed angle. Therefore, for an angle of 30°, the intercepted arc measures 60°.
Two inscribed angles intercept arcs of 80° and 100° respectively. What are their measures?
40° and 50° respectively.
50° and 40° respectively.
Both measure 40°.
Both measure 50°.
An inscribed angle measures half of its intercepted arc. Thus, an 80° arc yields a 40° angle and a 100° arc yields a 50° angle.
If an inscribed angle is formed by a diameter and a chord, what type of angle is it?
Straight angle
Acute angle
Obtuse angle
Right angle
By Thales' Theorem, an inscribed angle that intercepts a semicircle (formed by a diameter) is a right angle. This is a well-known result in circle geometry.
Three inscribed angles intercept the same arc in a circle. What can be concluded about these angles?
Their measures are proportional to the arc lengths.
They are congruent.
They are supplementary.
The sum of their measures is 180°.
The inscribed angle theorem ensures that all inscribed angles intercepting the same arc are congruent, regardless of their locations on the circle. This principle is often used to establish angle equality in proofs.
Chord AB and chord AC form an inscribed angle at A intercepting arc BC of 100°. What is the measure of angle A?
75°
25°
100°
50°
Angle A, being an inscribed angle intercepting a 100° arc, measures half of that arc, which is 50°. This is a direct and common application of the inscribed angle theorem.
If one inscribed angle intercepts an arc that is 90° larger than that of a second inscribed angle, what is the difference between the measures of the two angles?
30°
90°
15°
45°
Since the measure of an inscribed angle is half of its intercepted arc, a 90° difference in intercepted arcs results in a 45° difference in the corresponding inscribed angles.
An inscribed angle intercepts an arc measuring 120°. What is the measure of the inscribed angle?
90°
60°
30°
120°
Using the inscribed angle theorem, the angle is half of its intercepted arc. Therefore, an intercepted arc of 120° results in an inscribed angle of 60°.
Two inscribed angles intercept arcs that together sum to 180°. What can be deduced about the inscribed angles?
They are both right angles.
They must be complementary.
They are congruent.
They do not necessarily add up to 90°.
Even though the intercepted arcs sum to 180°, the inscribed angles are half their respective intercepted arcs and therefore do not automatically sum to 90° unless the arcs are equal. Each angle must be calculated individually.
How does the inscribed angle theorem explain the congruence of inscribed angles intercepting the same chord?
Inscribed angles intercepting the same chord are congruent regardless of their position.
Inscribed angles are congruent only if they occur in the same semicircle.
The inscribed angle is always double the chord's angle.
Central angles determine the congruence of inscribed angles.
The inscribed angle theorem guarantees that any inscribed angles intercepting the same chord (or arc) are congruent, regardless of where their vertices are located on the circle. This property is fundamental in many geometric proofs and problem-solving contexts.
In a cyclic quadrilateral, one inscribed angle intercepts an arc of 130°. What are the measures of this inscribed angle and its opposite angle?
130° and 50°
130° and 90°
65° and 65°
65° and 115°
An inscribed angle measures half of its intercepted arc, so an arc of 130° yields an angle of 65°. In a cyclic quadrilateral, opposite angles are supplementary, which means the angle opposite to 65° must be 115° (since 180° âˆ' 65° = 115°).
A circle has two arcs that together form the entire circumference. If an inscribed angle intercepting one arc measures 35°, what is the measure of the intercepted arc of the other segment?
250°
170°
290°
310°
An inscribed angle of 35° intercepts an arc of 70° (since the angle is half the intercepted arc). Since both arcs together make 360°, the measure of the other intercepted arc is 360° âˆ' 70° = 290°.
If an inscribed angle ∠ABC is formed by chords AB and AC, and a tangent at point C forms an angle with chord AC, what is the relationship between ∠ABC and the angle between chord AC and the tangent?
The tangent angle is half the inscribed angle.
They are congruent.
They are supplementary.
The inscribed angle is twice the tangent angle.
According to the Alternate Segment Theorem, the angle formed between a chord and a tangent through the point of contact is congruent to the inscribed angle in the alternate segment. This theorem establishes a direct relationship between tangent-chord angles and inscribed angles.
An inscribed angle intercepts an arc that is divided into two segments measuring 80° and 40°. What is the measure of the inscribed angle?
40°
60°
80°
20°
Even if the intercepted arc is subdivided, the inscribed angle depends on the total measure of the arc. Here, 80° + 40° equals 120°, and half of 120° is 60°, which is the measure of the inscribed angle.
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Study Outcomes

  1. Understand the definition and properties of inscribed angles in a circle.
  2. Analyze the relationship between inscribed angles and their intercepted arcs.
  3. Apply the Inscribed Angle Theorem to solve geometry problems.
  4. Evaluate problem-solving strategies for different configurations of inscribed angles.
  5. Demonstrate competence in translating geometric concepts into accurate diagram constructions.

Inscribed Angles Quiz - Practice Test Cheat Sheet

  1. Defining Inscribed Angles - An inscribed angle is formed by two chords that meet at a point on the circle's edge. The angle "inscribes" an arc between the other chord endpoints. Grasping this concept sets the foundation for all circle angle problems. Inscribed Angles Basics
  2. GeeksforGeeks: Inscribed Angles
  3. Inscribed Angle Theorem - The Inscribed Angle Theorem tells us an inscribed angle always measures half of its intercepted arc. For example, an arc spanning 80° corresponds to a 40° inscribed angle, making calculations a breeze. This relationship is a cornerstone for solving many circle geometry problems. Inscribed Angle Theorem
  4. MathBits: Inscribed Angles
  5. Congruent Inscribed Angles - Inscribed angles that intercept the same arc share equal measures and are therefore congruent. Spotting these equal angles helps you unlock missing measures in complex diagrams. This trick often appears in competition problems! Congruent Angles
  6. MathBits: Congruent Angles
  7. Right Angle Semicircle - Any inscribed angle that spans a semicircle (half the circle) will be a perfect 90°. This property is super handy for quickly identifying right angles without extra calculation. It also provides a quick shortcut in proofs. Semicircle Shortcut
  8. MathBits: Semicircle Angles
  9. Cyclic Quadrilateral Rule - In a cyclic quadrilateral (all four vertices on the circle), opposite angles always add up to 180°. This powerful fact helps you solve for unknown angles in four-sided figures inscribed in circles. It's a must-know for any circle geometry quiz! Cyclic Quads Explained
  10. MathBits: Cyclic Quadrilaterals
  11. Central vs. Inscribed Angles - A central angle's measure equals its intercepted arc, while an inscribed angle is exactly half that measure. Recognizing this link lets you switch between central and inscribed angles with confidence. This dual perspective is essential for mastering circle theorems. Angle Relationships
  12. Wikipedia: Inscribed Angle
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