Question

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.

Answer 1

Answer:

• m∠1=45 degrees
• m∠2=135 degrees
• m∠3=45 degrees
• m∠4=135 degrees

Step-by-step explanation:

Given that: 3(m∠1+m∠3) = m∠2+m∠4.

From the diagram:

• m∠1=m∠3 (Vertical Angles)
• m∠2=m∠4 (Vertical Angles)

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