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Chapter 3: Q11 (page 96)

Find the value of x.

Short Answer

Expert verified

The value of x is 75.

Step by step solution

01

Step 1. Label the given diagram.

The labelled diagram is:

02

Step 2. Description of step.

From the diagram it can be noticed that the angles 鈭�ABEand 鈭�ABCforms the linear pair.

Therefore, the sum of the angles 鈭�ABEand 鈭�ABCis 180掳.

Therefore, it can be obtained that:

鈭�ABE+鈭�ABC=180掳140掳+鈭�ABC=180掳鈭�ABC=180掳鈭�140掳鈭�ABC=40掳

Therefore, the measure of the angle 鈭�ABCis 40掳.

03

Step 3. Find the value of x.

Now, by using the exterior angle theorem it can be noticed that:

鈭�ABC+鈭�BAC=鈭�ACD

Therefore, the value of x can be obtained as:

鈭�ABC+鈭�BAC=鈭�ACD40掳+35掳=x掳75掳=x掳鈬�75=x

Therefore, the value of x is 75.

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