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Chapter 2: Q21. (page 53)

Find the value of x.

Short Answer

Expert verified

The value of x is 25.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Label the given figure.

Label the given figure as shown below:

From the diagram, it can be noticed that:

鈭�DOF=4x掳,鈭�AOB=64掳 and鈭�BOC=36掳

03

Step 3. Write the relation between the angles.

From the given diagram it can be noticed that the angles AOC and DOF are vertically opposite angles.

Therefore, the angles AOC and DOF are congruent angles. Therefore, the angles AOC and DOF have the same measure.

04

Step 4. Find the value of the angle AOC.

From the diagram it can be noticed that:

鈭�AOC=鈭�AOB+鈭�BOC.

Therefore,

鈭�AOC=鈭�AOB+鈭�BOC=64掳+36掳=100掳

Therefore, the measure of the angle AOC is 100掳.

05

Step 3. Description of step.

Find the value of x by using the fact that the angles AOC and DOF have the same measure.

4x=100x=1004x=25

Therefore, the value of x is 25.

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Most popular questions from this chapter

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only if

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Proof:
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