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Q2.

Expert-verified

Geometry

Found in: Page 341

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

Find the measure of central $∠ 1 .$

a. The measure of angle $∠ 1$ is $80 ° .$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information:

The given figure is,

Step 2. Concept used:

In the circle the angle of the circle can be calculated by subtracting the total angle of the circle by its given value.

Step 3. Applying the concept:

Here, we can see that in the figure.

Measure of arc,

$\begin{array}{l} = 360^{\circ} - 280^{\circ} \\ = 80^{\circ} \end{array}$

As we know,

$\begin{array}{l} ∠ 1 = \\ = 80^{\circ} \end{array}$ measure of arc

Therefore, the measure of the angle $∠ 1$ is $80 ° .$

Most popular questions for Math Textbooks

For each exercise draw $⊙ O$ with radius $12$ . Then draw radii $\bar{O A}$ and to $\bar{O B}$ form an angle with the measure named. Find the length of $\bar{A B}$ .

a. $m ∠ A O B = 90 °$

Name the 4 radii (none are drawn in the diagram).

Using the letters shown in the diagram, name:

a. two central angles b. a semicircle c. two minor arcs d. two major arcs

Draw a diagram similar to the one shown, but much larger. Carefully draw the perpendicular bisectors of $\bar{A B}$ and $\bar{B C}$ .

The perpendicular bisect in a point. Where does that point to be?
Write an argument that justifies your answer to part (a).

$(a) .$ What do you think is true of common external tangents $\bar{A B}$ and $\bar{C D}$ $?$ prove it.

$(b) .$ Will your results in part $(a)$ be true if the circles are congruent $?$

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