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Q9

Expert-verified

Geometry

Found in: Page 46

Book edition Student Edition

Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Pages 227 pages

ISBN 9780395977279

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Short Answer

State the number that is paired with the bisector of $∠ C D E$ .

The number paired with the bisector of $∠ C D E$ is $60 °$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. State the given information.

$∠ C D F = 80^{\circ}$

$∠ E D F = 40 °$

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 $∠ C D E$ is shown in Figure-1 here,

Suppose z is the number paired with the bisector of $∠ C D E$ as shown in Figure-2 here,

Assume $∠ B D F = z °$ .

Let $∠ C D B = x °$

That implies

$∠ B D E = x °$ [ since DB is bisector of $∠ C D E$ ]

Then,

$∠ E D F + ∠ B D E + ∠ C D B = 40 ° + x ° + x °$

Again,

$∠ E D F + ∠ B D E + ∠ C D B = ∠ C D F$

$= 80 °$

Then,

$40 ° + x ° + x ° = 80 °$

$40 ° + 2 x ° = 80 °$

$2 x ° = 40 °$

$x ° = 20 °$

Step 3. State the conclusion.

It is known that $∠ B D F = ∠ B D E + ∠ E D F$ , then,

$∠ B D F = ∠ B D E + ∠ E D F$

$z ° = 40 ° + 20 °$

$= 60 °$

Therefore, the number paired with the bisector of $∠ C D E$ is $60 °$

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