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Chapter 2: Q7 (page 41)

Copy everything shown and supply missing statements and reasons.

Given: ∠AODas shown

Prove: m∠AOD=m∠1+m∠2+m∠3

Proof:

Short Answer

Expert verified

From the given figure, it can be observed that ∠AOCand ∠3are adjacent angles.

m∠AODcan be written as the sum of two adjacent angles, that is, m∠AOCand m∠3.

m∠AOD=m∠AOC+m∠3

Step by step solution

01

Step 1. Add adjacent angles.

From the given figure, it can be observed that ∠AOCand ∠3are adjacent angles.

m∠AODcan be written as the sum of two adjacent angles, that is, m∠AOCand m∠3.

m∠AOD=m∠AOC+m∠3

02

Step 2. Add adjacent angles.

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

m∠AOCcan be written as the sum of two adjacent angles, that is, m∠1and m∠2.

m∠AOC=m∠1+m∠2

03

Step 3. Apply substitution property of algebra.

Substitutem∠1+m∠2 for m∠AOCinto step 1.

m∠AOD=m∠AOC+m∠3

=m∠1+m∠2+m∠3

Hence it is proved that m∠AOD=m∠1+m∠2+m∠3.

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