Q33. Find the value of x and y for ea... [FREE SOLUTION]

魅影直播

Geometry

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

$Math Studyset 魅影直播 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 2: Q33. (page 54)

Find the value of x and y for each diagram.

Short Answer

Expert verified

The values of x and y are 33 and 66 respectively.

Step by step solution

Step 1. Label the given diagram.

Label the figure as shown:

Step 2. Write the relation between the angles BOF and AOE.

From the given diagram it can be noticed that the angles BOF and AOE are the vertically opposite angles.

Therefore, $鈭� B O F = 鈭� A O E$

Step 3. Find the value of x.

Find the value of x by using the fact that $鈭� B O F = 鈭� A O E$ .

Therefore,

$鈭� B O F = 鈭� A O E 2 x - 16 = 50 2 x = 50 + 16 2 x = 66 x = \frac{66}{2} x = 33$

Therefore, the value of x is 33.

Step 4. Find the measure of the angle COF.

As the value of x is 33 and the measure of the angle COF is x.

Therefore, the measure of the angle COF is:

$x = 33$

Therefore, the measure of the angle COF is 33掳.

Step 5. Write the relation between the angles COF and EOD.

From the diagram, it can be noticed that the angles COF and EOD are vertically opposite angles.

Therefore, $鈭� C O F = 鈭� E O D$ .

Step 6. Find the value of y.

As, $鈭� C O F = 鈭� E O D$ .

Therefore,

$鈭� C O F = 鈭� E O D 33 = 3 (33) - y 33 = 99 - y y = 99 - 33 y = 66$

Therefore, the value of y is 66.

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Statements	Reasons
1. $\overset{鈫�}{O A} 鈯� \overset{鈫�}{O C}$	1. _________
2. $m 鈭� A O C = 90$	2. Def. of $鈯�$ lines
3. $m 鈭� A O B + m 鈭� B O C = m 鈭� A O C$	3._________
4. _________	4. Substitution Prop.
5. _________	5. Def. of comp. $鈭� s$

魅影直播

Find the value of x and y for each diagram.

Short Answer

Step by step solution

Step 1. Label the given diagram.

Step 2. Write the relation between the angles BOF and AOE.

Step 3. Find the value of x.

Step 4. Find the measure of the angle COF.

Step 5. Write the relation between the angles COF and EOD.

Step 6. Find the value of y.

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