Chapter 2: Q10 (page 42)

Copy everything shown and supply missing statements and reasons.
Given: $m ∠ 4 + m ∠ 6 = 180$
Prove: $m ∠ 5 = m ∠ 6$
Proof:

Short Answer

Expert verified

Step by step solution

Step 1. Apply the definition of linear pair of angles.

When two lines intersect each other at a single point, they formed linear pair of angles. The sum of the linear pair of angles is always 180.

Step 2. Description of step.

From the given figure, it can be observed that $∠ 4$ and $∠ 5$ form a linear pair of angles, that is, the sum of $∠ 4$ and $∠ 5$ is 180.

$m ∠ 4 + m ∠ 5 = 180$

Step 3. Apply substitution property of algebra.

Substitute $m ∠ 4 + m ∠ 5$ for 180 into $m ∠ 4 + m ∠ 6 = 180$ .

$m ∠ 4 + m ∠ 5 = m ∠ 4 + m ∠ 6$

Step 4. Reflexive property.

By reflexive property, $m ∠ 4 = m ∠ 4$ .

Step 4. Apply subtraction property of algebra to step 3.

If $a = b$ and $c = d$ , then $a - c = b - d$ .

$\begin{matrix} m ∠ 4 + m ∠ 5 = m ∠ 4 + m ∠ 6 \\ m ∠ 5 = m ∠ 6 \end{matrix}$

Hence, it is proved that $m ∠ 5 = m ∠ 6$ .

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Copy everything shown and supply missing statements and reasons.
Given: $m ∠ 4 + m ∠ 6 = 180$
Prove: $m ∠ 5 = m ∠ 6$
Proof:

Short Answer

Step by step solution

Step 1. Apply the definition of linear pair of angles.

Step 2. Description of step.

Step 3. Apply substitution property of algebra.

Step 4. Reflexive property.

Step 4. Apply subtraction property of algebra to step 3.

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Copy everything shown and supply missing statements and reasons.Given:m∠4+m∠6=180Prove: m∠5=m∠6Proof:

Short Answer

Step by step solution

Step 1. Apply the definition of linear pair of angles.

Step 2. Description of step.

Step 3. Apply substitution property of algebra.

Step 4. Reflexive property.

Step 4. Apply subtraction property of algebra to step 3.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Probability and Statistics

Logic and Functions

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

Copy everything shown and supply missing statements and reasons.
Given: $m ∠ 4 + m ∠ 6 = 180$
Prove: $m ∠ 5 = m ∠ 6$
Proof: