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Chapter 2: Q9 (page 46)

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

Short Answer

Expert verified

The number paired with the bisector of 鈭�CDEis 60掳.

Step by step solution

01

Step 1. State the given information.

鈭�CDF=80鈭�

鈭�EDF=40掳

02

Step 2. State the assumptions and the calculations.

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

The required number that is paired with the bisector of 鈭�CDEis shown in Figure-1 here,

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

Assume 鈭�BDF=z掳.

Let 鈭�CDB=x掳

That implies

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

Then,

鈭�EDF+鈭�BDE+鈭�CDB=40掳+x掳+x掳

Again,

鈭�EDF+鈭�BDE+鈭�CDB=鈭�CDF

=80掳

Then,

40掳+x掳+x掳=80掳

40掳+2x掳=80掳

2x掳=40掳

x掳=20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=40掳+20掳

=60掳

Therefore, the number paired with the bisector of 鈭�CDEis 60掳

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