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Anvisha [2.4K]
2 years ago
5

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

Mathematics
2 answers:
mixer [17]2 years ago
8 0

Hello and Good Morning/Afternoon

<u>Let's take this problem step-by-step</u>:

<u>What does this problem give us</u>:

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

<u>What does this problem want us to find</u>:

  • measure of ∠6
  • measure of ∠7

<u>Let's solve:</u>

  • ∠6

           ⇒ by the <em>vertical angle theorem</em> 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

<em>Definitions</em>

  • <em>Vertical Angle Theorem: two opposite angles formed by intersecting lines are equal</em>

<em />

<u>Answer:</u>

  • <u>∠6 = 52°</u>
  • <u>∠7 = 128°</u>

<em />

Hope that helps!

#LearnwithBrainly

Andreyy892 years ago
5 0

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

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