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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 3: Q14. (page 114)

In the diagram $\overset{\leftrightarrow}{AB}$ bisects $∠ D H F, \overset{\leftrightarrow}{A B} ⊥ \bar{G H}, \overset{\leftrightarrow}{A B} ∥ \overset{\leftrightarrow}{C D},$ and $m ∠ A H D = 60^{\circ}$ . Find the measure of each angle.
$∠ FHD$

Short Answer

Expert verified

The angle $∠ F H D$ is $120^{\circ}$

Step by step solution

01

Step 1. Observe the diagram.

Here, $∠ A H D = 60^{\circ}, \overset{\leftrightarrow}{A B} ⊥ \bar{G H}, \overset{\leftrightarrow}{A B} ∥ \overset{\leftrightarrow}{C D}$ and $\overset{\leftrightarrow}{A B}$ bisects $∠ D H F$ .

02

Step 2. Show the calculation.

From the figure,

$∠ A H D = \frac{1}{2} ∠ F H D ∠ F H D = 2 \times ∠ A H D = 2 \times 60^{\circ} = 120^{\circ}$

03

Step 3. State the conclusion.

Therefore, $∠ F H D = 120^{\circ}$

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