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Chapter 2: Q23. (page 71)

In the diagram, OB鈫�bisects 鈭�AOCand EC鈫�鈯�OD鈫�.

Find the value of x.

尘鈭�2 = 6x + 9, m鈭�5 = 2x + 49

Short Answer

Expert verified

The value of x is 10.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is :

02

Step 2. Write the relation between the angles ∠2 and ∠5.

From the given diagram it can be noticed that the angles鈭�2and鈭�5are the vertical angles.

Therefore, by using the theorem for vertical angles it can be said that the angles鈭�2and鈭�5have the same measure.

That implies, m鈭�2=m鈭�5.

Therefore, the relation between the angles 鈭�2 and 鈭�5 is m鈭�2=m鈭�5.

03

Step 3. Find the value of x.

As, 尘鈭�2 =尘鈭�5, 尘鈭�2 =6x + 9 and尘鈭�5 = 2x + 49.

Therefore, the value of x is given by :

m鈭�2=m鈭�5

6x+9=2x+49

6x鈭�2x=49鈭�9

4x=40

x=404

x=10

Therefore, the value of x is 10.

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Most popular questions from this chapter

Copy everything shown and write a two-column proof.

Given:m鈭�SRT=m鈭�STR;

m鈭�3=m鈭�4

Proof:m鈭�1=m鈭�2

Justify each step.

3a2=653a=125a=45

Write each biconditional as two conditionals that are converses of each other.

Points are collinear if and only if they all lie in one line.

Justify each statement with a property from algebra or property of congruence.

If AB=CD,CD=EFand EF=23then AB=23.

State which postulate, definition, or theorem justifies the statement about the diagram.

If D is the midpoint of BC炉, then BD炉鈮�DC炉.
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