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Chapter 2: Q10 (page 46)

State the number that is paired with the bisector of ∠CDE.

Short Answer

Expert verified

The number paired with the bisector of ∠CDEis 75°.

Step by step solution

01

Step 1. State the given information.

∠CDF=120°

∠EDF=30°

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 ∠CDEis shown in Figure-1 here,

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

Assume ∠BDF=z°.

Let ∠CDB=x°

That implies

∠BDE=x° [ since DB is the bisector of ∠CDE]

Then,

∠EDF+∠BDE+∠CDB=30°+x°+x°

Again,

∠EDF+∠BDE+∠CDB=∠CDF

=120°

Then,

30°+x°+x°=120°

30°+2x°=120°

2x°=90°

x°=45°

03

Step 3. State the conclusion.

It is known that ∠BDF=∠BDE+∠EDF, then,

∠BDF=∠BDE+∠EDF

z°=30°+45°

=75°

Therefore, the number paired with the bisector of ∠CDEis 75°

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