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Chapter 2: Q11 (page 46)

State the number that is paired with the bisector of 鈭�CDE.

Short Answer

Expert verified

The number paired with bisector of 鈭�CDE is 70掳.

Step by step solution

01

Step 1. Observe the diagram.

The required number is paired with the bisector of 鈭�CDEshown in Figure-1 here.

02

Step 2. State the assumptions and the calculations.

For the calculation, the concept used is the definition of the bisector angle.

Suppose z is the number paired with the bisector of 鈭�CDEas shown in Figure-2 here,

From Figure-2:

鈭�CDF=122掳

鈭�EDF=18掳

Assume 鈭�BDF=z掳.

Let 鈭�CDB=x掳

That implies

鈭�BDE=x掳 [ since DB is the bisector of 鈭�CDE]

Then,

鈭�EDF+鈭�BDE+鈭�CDB=18掳+x掳+x掳

Again,

鈭�EDF+鈭�BDE+鈭�CDB=鈭�CDF

=122掳

Then,

18掳+x掳+x掳=122掳

18掳+2x掳=122掳

2x掳=104掳

x掳=52掳

03

Step 3. State the conclusion.

It is known that 鈭�BDF=鈭�BDE+鈭�EDF, then,

鈭�BDF=鈭�BDE+鈭�EDF

z掳=18掳+52掳

=70掳

Therefore, the number paired with the bisector of 鈭�CDEis70掳

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