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Chapter 2: Q10 (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 75掳.

Step by step solution

01

Step 1. State the given information.

鈭�CDF=120掳

鈭�EDF=30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 as shown in Figure-2 here,

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=30掳+x掳+x掳

Again,

鈭�EDF+鈭�BDE+鈭�CDB=鈭�CDF

=120掳

Then,

30掳+x掳+x掳=120掳

30掳+2x掳=120掳

2x掳=90掳

x掳=45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=30掳+45掳

=75掳

Therefore, the number paired with the bisector of 鈭�CDEis 75掳

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