Use the diagram to find the angle measures that satisfy each case. Find the measures of all four angles if 3·(m∠1+m∠3) = m∠2+m∠4

Question

3 years ago

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1 answer:

Doss [256] · Answer 1 · 2022-08-13T22:29:40+03:00

Answer:

Step-by-step explanation:

Given that: 3(m∠1+m∠3) = m∠2+m∠4.

From the diagram:

Therefore:

3(m∠1+m∠1) = m∠2+m∠2

3(2m∠1)=2m∠2

Divide both sides by 2

3m∠1=m∠2

m∠1+m∠2=180 (Linear Postulate)

Therefore:

m∠1+3m∠1=180

4m∠1=180

Divide both sides by 4

m∠1=45 degrees

Since m∠1=m∠3

m∠3=45 degrees

Recall: m∠1+m∠2=180 (Linear Postulate)

45+m∠2=180

m∠2=180-45

m∠2=135 degrees

Since m∠2=m∠4

m∠4=135 degrees