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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

01

Step 1. Label the given diagram.

Label the figure as shown:

02

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�BOF=鈭�AOE

03

Step 3. Find the value of x.

Find the value of x by using the fact that 鈭�BOF=鈭�AOE.

Therefore,

鈭�BOF=鈭�AOE2x-16=502x=50+162x=66x=662x=33

Therefore, the value of x is 33.

04

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.

05

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�COF=鈭�EOD.

06

Step 6. Find the value of y.

As, 鈭�COF=鈭�EOD.

Therefore,

鈭�COF=鈭�EOD33=333-y33=99-yy=99-33y=66

Therefore, the value of y is 66.

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