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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: Q15. CUR (page 114)

In the diagram $\overset{\leftrightarrow}{A B}$ 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.
$∠ A H G$

Short Answer

Expert verified

The angle $∠ A H G$ is $90^{\circ}$

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,

$\overset{\leftrightarrow}{A B} ⊥ \bar{G H}$

$\overset{\leftrightarrow}{A H} ⊥ \bar{G H}$

Two perpendicular lines make an angle of $90^{\circ}$ .

Hence the angle $∠ A H G = 90^{\circ}$

03

Step 3. State the conclusion.

Therefore, $∠ A H G = 90^{\circ}$

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