Chapter 3: Q18. (page 114)

In the diagram $\overset{\leftrightarrow}{AB}$ bisects $∠ DHF$ , $\overset{\leftrightarrow}{AB} ⊥ \bar{GH}$ , $\overset{\leftrightarrow}{AB} ∥ \overset{\leftrightarrow}{CD}$ , and $m ∠ AHB= 60^{\circ}$ . Find the measure of each angle.
$∠ BHC$ .

Short Answer

Expert verified

The angle $∠ BHC$ is $60^{\circ}$ .

Step by step solution

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 $∠ D H F$ .

Step 2. Show the calculation.

From the figure and the data,

$∠ B H C$ and $∠ A H F$ are vertical angles and they are congruent.

$∠ A H F = ∠ A H D = 60^{\circ}$

Since, $\overset{\leftrightarrow}{A B}$ bisects $∠ D H F$ .

Hence the angle $∠ B H C = 60^{\circ}$ .

Step 3. State the conclusion.

Therefore, $∠ B H C = 60^{\circ}$ .

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In the diagram $\overset{\leftrightarrow}{AB}$ bisects $∠ DHF$ , $\overset{\leftrightarrow}{AB} ⊥ \bar{GH}$ , $\overset{\leftrightarrow}{AB} ∥ \overset{\leftrightarrow}{CD}$ , and $m ∠ AHB= 60^{\circ}$ . Find the measure of each angle.
$∠ BHC$ .

Short Answer

Step by step solution

Step 1. Observe the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

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In the diagram AB↔bisects ∠DHF, AB↔⊥GH¯, AB↔∥CD↔, and m∠AHB=60∘. Find the measure of each angle.∠BHC.

Short Answer

Step by step solution

Step 1. Observe the diagram.

Step 2. Show the calculation.

Step 3. State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Probability and Statistics

Geometry

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

In the diagram $\overset{\leftrightarrow}{AB}$ bisects $∠ DHF$ , $\overset{\leftrightarrow}{AB} ⊥ \bar{GH}$ , $\overset{\leftrightarrow}{AB} ∥ \overset{\leftrightarrow}{CD}$ , and $m ∠ AHB= 60^{\circ}$ . Find the measure of each angle.
$∠ BHC$ .