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.
