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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 9: Q7. (page 341)

In exercises $2 - 7$ find the measure of the arc.
$\overset{⏜}{C D B}$

Short Answer

Expert verified

a. The measure of an arc $\overset{⏜}{C D B}$ is $280 .$

Step by step solution

01

Step 1. Given information:

The given figure is,

02

Step 2. Concept used:

Following properties are used here,

The arc length of a circle can be calculated with the radius and central angle.

03

Step 3. Applying the concept:

Here, in the figure

$\begin{array}{l} ∠ C D B = 360^{\circ} - ∠ B O C \\ {=360}^{\circ} - 80^{\circ} \\ =28 0^{\circ} \end{array}$

Since

$\begin{array}{l} m \overset{⏜}{C D B} = m ∠ C D B \\ =280 \end{array}$

Therefore, the measure of arc $C D B$ is $280 .$

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Most popular questions from this chapter

$\bar{J T}$ is tangent to $⊙$ $O$ at $T$ . Complete.

If $m ∠ T O J = 60$ and $O T = 6$ , then $J O = ?$

Name three radii of $⊙ o$ .

Use a compass to draw a large $⊙ o .$ Draw a central $∠ A O B .$ .

a. draw three other points $P, Q$ and $R$ that are on $⊙ o$ but not on $\overset{⏜}{A B}$ .

then draw $∠ A P B, ∠ A Q B$ and $∠ A R B$ .

b. Use a protractor to find $m ∠ A O B, m ∠ A P B, m ∠ A Q B$ and $m ∠ A R B$ .

c. What is the relationship between $m ∠ A P B, m ∠ A Q B$ and $m ∠ A R B ?$

What is the relationship between $m ∠ A O B$ and $m ∠ A P B ?$

For each exercise draw a circle and inscribe the polygon in the circle.

e. An acute isosceles triangle.

a. Draw a circle. Place points A,B, and C on it in such positions that

\ $[m \overset{⏜}{A B} + m \overset{⏜}{B C} \]$ does not equal

b. Does your example in part (a) contradict Postulate $16$ ?

See all solutions

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