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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 1: Q20 (page 20)

State the measure of each angle.
$∠ C O F$

Short Answer

Expert verified

The measure of $∠ C O F$ is $30 °$ .

Step by step solution

01

Step 1. Apply protractor postulate.

On $\bar{A H}$ in a given plane, choose any point O between A and B.

Consider rays, $\bar{O A}$ and $\bar{O H}$ which are drawn from point O on $\bar{A H}$ .

These rays results in pairing with the angles from 0 to 180 in such a way that:

The line $\bar{O A}$ is paired with 0, and $\bar{O H}$ with 180.

If $\bar{O C}$ is paired with x, and $\bar{O F}$ with y, then $m ∠ C O F = |x - y|$ .

02

Step 2. Observe the figure below and write the values of OG and OF.

It can be observed from the figure that, $\bar{O C}$ is 90 and $\bar{O F}$ is 120.

03

Step 3. Calculate m∠COF

$\begin{array}{l} m ∠ C O F = |90 - 120| \\ = |- 30| \\ = 30 ° \end{array}$

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