Question

Can someone PLEASE ANSWER BOTH THESE QUESTIONS!!!!!!!!

Answer 1

Answer:

52º, 128º

Step-by-step explanation:

8. Because ∠6 is an opposite angle to ∠5, ∠6=∠5=52º;

9. Because line a//line b, ∠6=∠4=52º, so ∠7=180º–52º=128º

Answer 2

Hello and Good Morning/Afternoon

Let's take this problem step-by-step:

What does this problem give us:

• a || b     ⇒    a is parallel to b
• c           ⇒    is a transversal
• m∠5     ⇒     52°

What does this problem want us to find:

• measure of ∠6
• measure of ∠7

Let's solve:

• ∠6

           ⇒ by the vertical angle theorem is equal in measure to ∠5

               ⇒ ∠6 = 52°

• ∠7

           ⇒ lines a and b are parallel

               ⇒ the corresponding angles on both lines formed by the

                    transversal are equal

                         i.e. m∠2 = m∠3, m∠7 = m∠8

           ⇒ ∠8 is on a straight line with ∠6

                      $\hookrightarrow angle8 +angle6 = 180\\\hookrightarrow angle8 + 52 = 180\\\hookrightarrow angle8 =128$

           ⇒ since m∠8 is equal to m∠7

              ⇒ m∠7 = 128

Definitions

• Vertical Angle Theorem: two opposite angles formed by intersecting lines are equal

Answer:

• ∠6 = 52°
• ∠7 = 128°

Hope that helps!

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