Unit 10: Circles Homework 7: Arc & Angle Measures formed by Chords, Secants, & Tangents

This worksheet focuses on solving problems related to arc and angle measures formed by chords, secants and tangents in circles. It contains ten questions that require students to apply their knowledge of circle geometry and trigonometry.

Highlight: The worksheet assumes that all segments that appear to be tangent are indeed tangent to the circle.

The problems cover a range of concepts, including:

1. Calculating measures of inscribed angles
2. Finding arc measures
3. Determining central angle measures
4. Solving for unknown variables in circle-related equations

Example: In question 1, students are asked to find mZYZV. The solution shows that (144+114) / 2 = 129°, demonstrating the relationship between inscribed angles and the arcs they intercept.

Vocabulary:

• Chord: A line segment with endpoints on a circle
• Secant: A line that intersects a circle at two points
• Tangent: A line that touches a circle at exactly one point

The worksheet provides a mix of straightforward calculations and more complex problem-solving tasks. For instance, questions 9 and 10 require students to solve equations to find the value of x.

Definition: An inscribed angle is an angle formed by two chords with a vertex on the circle. Its measure is half the measure of the central angle that subtends the same arc.

The solutions are clearly presented, showing each step of the calculation process. This approach helps students understand the reasoning behind each solution and reinforces the mathematical concepts involved in arc and angle measures formed by chords, secants and tangents.