Chapter 2: Q7 (page 41)

Copy everything shown and supply missing statements and reasons.
Given: $∠ A O D$ as shown
Prove: $m ∠ A O D = m ∠ 1 + m ∠ 2 + m ∠ 3$
Proof:

Short Answer

Expert verified

From the given figure, it can be observed that $∠ A O C$ and $∠ 3$ are adjacent angles.

$m ∠ A O D$ can be written as the sum of two adjacent angles, that is, $m ∠ A O C$ and $m ∠ 3$ .

$m ∠ A O D = m ∠ A O C + m ∠ 3$

Step by step solution

Step 1. Add adjacent angles.

From the given figure, it can be observed that $∠ A O C$ and $∠ 3$ are adjacent angles.

$m ∠ A O D$ can be written as the sum of two adjacent angles, that is, $m ∠ A O C$ and $m ∠ 3$ .

$m ∠ A O D = m ∠ A O C + m ∠ 3$

Step 2. Add adjacent angles.

From the given figure, it can be observed that $∠ 1$ and $∠ 2$ are adjacent angles.

$m ∠ A O C$ can be written as the sum of two adjacent angles, that is, $m ∠ 1$ and $m ∠ 2$ .

$m ∠ A O C = m ∠ 1 + m ∠ 2$

Step 3. Apply substitution property of algebra.

Substitute $m ∠ 1 + m ∠ 2$ for $m ∠ A O C$ into step 1.

$m ∠ A O D = m ∠ A O C + m ∠ 3$

$= m ∠ 1 + m ∠ 2 + m ∠ 3$

Hence it is proved that $m ∠ A O D = m ∠ 1 + m ∠ 2 + m ∠ 3$ .

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Copy everything shown and supply missing statements and reasons.
Given: $∠ A O D$ as shown
Prove: $m ∠ A O D = m ∠ 1 + m ∠ 2 + m ∠ 3$
Proof:

Short Answer

Step by step solution

Step 1. Add adjacent angles.

Step 2. Add adjacent angles.

Step 3. Apply substitution property of algebra.

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Copy everything shown and supply missing statements and reasons.Given: ∠AODas shown Prove: m∠AOD=m∠1+m∠2+m∠3Proof:

Short Answer

Step by step solution

Step 1. Add adjacent angles.

Step 2. Add adjacent angles.

Step 3. Apply substitution property of algebra.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Mechanics Maths

Decision Maths

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Copy everything shown and supply missing statements and reasons.
Given: $∠ A O D$ as shown
Prove: $m ∠ A O D = m ∠ 1 + m ∠ 2 + m ∠ 3$
Proof: