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Chapter 2: Q10 (page 42)

Copy everything shown and supply missing statements and reasons.

Given:m鈭�4+m鈭�6=180

Prove: m鈭�5=m鈭�6

Proof:

Short Answer

Expert verified

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 by step solution

01

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.

02

Step 2. Description of step.

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

m鈭�4+m鈭�5=180

03

Step 3. Apply substitution property of algebra.

Substitute m鈭�4+m鈭�5for 180 into m鈭�4+m鈭�6=180.

m鈭�4+m鈭�5=m鈭�4+m鈭�6

04

Step 4. Reflexive property.

By reflexive property, m鈭�4=m鈭�4.

05

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

If a=band c=d, then a鈭�c=b鈭�d.

m鈭�4+m鈭�5=m鈭�4+m鈭�6m鈭�5=m鈭�6

Hence, it is proved that m鈭�5=m鈭�6.

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