Geometry

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

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 2: Q25. (page 71)

In the diagram, $\overset{鈫�}{O B}$ bisects $鈭� A O C$ and $\overset{鈫�}{E C} 鈯� \overset{鈫�}{O D}$ .
Find the value of $x$ .
localid="1649243329006" $m 鈭� 1 = x - 8$ , width="99">m鈭�2=2x+5, $m 鈭� 4 = 3 x - 26$

Short Answer

Expert verified

The value of $x$ is 31.

Step by step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the relation between the angles ∠1 and ∠2.

As, $\overset{鈫�}{E C} 鈯� \overset{鈫�}{O D}$ , therefore the lines $E C$ and $O D$ are perpendicular lines.

Therefore, by using the definition of perpendicular lines it can be said that the measures of the angle $鈭� D O E$ is $90 掳$ .

That implies, $m 鈭� D O E = 90 掳$ .

Now, by using the angle addition postulate it can be said that $m 鈭� D O E = m 鈭� 1 + m 鈭� 2$ .

Therefore, the relation between the angles $鈭� 1$ and $鈭� 2$ is:

$\begin{matrix} m 鈭� D O E = m 鈭� 1 + m 鈭� 2 \\ 90 = m 鈭� 1 + m 鈭� 2 \end{matrix}$

- Find the value of x.

As, $m 鈭� 1 + m 鈭� 2 = 90$ , $m 鈭� 1 = x 鈭� 8$ and $m 鈭� 2 = 2 x + 5$ .

Therefore, the value of $x$ is given by:

localid="1649244885505" $m 鈭� 1 + m 鈭� 2 = 90 x 鈭� 8 + 2 x + 5 = 90 3 x 鈭� 3 = 90 3 x = 90 + 3 3 x = 93 x = \frac{93}{3} x = 31$

Therefore, the value of $x$ is 31.

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91影视

In the diagram, $\overset{鈫�}{O B}$ bisects $鈭� A O C$ and $\overset{鈫�}{E C} 鈯� \overset{鈫�}{O D}$ .
Find the value of $x$ .
localid="1649243329006" $m 鈭� 1 = x - 8$ , width="99">m鈭�2=2x+5, $m 鈭� 4 = 3 x - 26$

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Write the relation between the angles ∠1 and ∠2.

- Find the value of x.

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91影视

In the diagram, OB鈫�bisects 鈭�AOCand EC鈫�鈯�OD鈫�.Find the value of x.localid="1649243329006" m鈭�1=x-8, width="99">m鈭�2=2x+5,m鈭�4=3x-26

Short Answer

Step by step solution

Step 1. Observe the given diagram.

Step 2. Write the relation between the angles ∠1 and ∠2.

- Find the value of x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the diagram, $\overset{鈫�}{O B}$ bisects $鈭� A O C$ and $\overset{鈫�}{E C} 鈯� \overset{鈫�}{O D}$ .
Find the value of $x$ .
localid="1649243329006" $m 鈭� 1 = x - 8$ , width="99">m鈭�2=2x+5, $m 鈭� 4 = 3 x - 26$