Chapter 3: Q22. (page 114)

In the diagram $\overset{\leftrightarrow}{AB}$ bisects $∠ DHF$ , $\overset{\leftrightarrow}{AB} ⊥ \bar{GH}$ , $\overset{\leftrightarrow}{AB} ∥ \overset{\leftrightarrow}{CD}$ , and role="math" localid="1647713022816" $m ∠ AHB= 60 °$ . Find the measure of each angle.
$∠ HCD$

Short Answer

Expert verified

The angle $∠ HCD$ is $60 °$ .

Step by step solution

Step 1. Observe the diagram.

Here, $∠ A H D = 60 °$ , $\overset{\leftrightarrow}{A B} ⊥ \bar{G H}$ , $\overset{\leftrightarrow}{A B} ∥ \overset{\leftrightarrow}{C D}$ 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.

$∠ B H C = ∠ A H F = 60 °$

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

$∠ B H C = ∠ H C D = 60 °$

Hence the angle $∠ H C D = 60 °$ .

Step 3. State the conclusion.

Therefore, $∠ H C D = 60 °$ .

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Statement	Reason
1. $k ∥ l$	Given
2. $∠ 3 ≅ ∠ 2$	If two parallel lines are cut by transversal then alt. int. $∠ s$ are $≅$
3. $∠ 1 ≅ ∠ 3$	Vert. $∠ s$ are $≅$
4. $∠ 1 ≅ ∠ 2$	Transitive Property

In the diagram $\overset{\leftrightarrow}{AB}$ bisects $∠ DHF$ , $\overset{\leftrightarrow}{AB} ⊥ \bar{GH}$ , $\overset{\leftrightarrow}{AB} ∥ \overset{\leftrightarrow}{CD}$ , and role="math" localid="1647713022816" $m ∠ AHB= 60 °$ . Find the measure of each angle.
$∠ HCD$

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 role="math" localid="1647713022816" m∠AHB=60°. Find the measure of each angle.∠HCD

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

Probability and Statistics

Geometry

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

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 role="math" localid="1647713022816" $m ∠ AHB= 60 °$ . Find the measure of each angle.
$∠ HCD$