Do ∠6 and ∠7 form a linear pair? What is the relation between ∠6 and ∠8?
Measures: m∠6=m∠8 = 73 and m∠7=107. Theorem: Supplement Theorem and Vertical Angles Theorem.
Practice makes perfect
We are given the following system of equations.
m∠6=2x-21 m∠7=3x-34
Additionally, from the diagram below, we can see that ∠6 and ∠7 form a linear pair.
Hence, using the Supplement Theorem we obtain that m∠6 + m∠7=180. We can substitute the expressions for m∠6 and m∠7 (given in the initial system) into this last equation and solve it for x.
Now, we substitute x= 47 into the equations of the initial system to find m∠6 and m∠7.
m∠6=2( 47)-21 m∠7=3( 47)-34
⇒
m∠6=73 m∠7=107
Now, we just need to find m∠8. However, from the diagram we see that ∠6 and ∠8 are vertical angles. Hence, using the Vertical Angles Theorem we conclude that m∠8= m∠6=73.
