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Chapter 2: Q9 (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 60°.

Step by step solution

01

Step 1. State the given information.

∠CDF=80∘

∠EDF=40°

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 ∠CDEas shown in Figure-2 here,

Assume ∠BDF=z°.

Let ∠CDB=x°

That implies

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

Then,

∠EDF+∠BDE+∠CDB=40°+x°+x°

Again,

∠EDF+∠BDE+∠CDB=∠CDF

=80°

Then,

40°+x°+x°=80°

40°+2x°=80°

2x°=40°

x°=20°

03

Step 3. State the conclusion.

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

∠BDF=∠BDE+∠EDF

z°=40°+20°

=60°

Therefore, the number paired with the bisector of ∠CDEis 60°

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