Answer:
Part a) consecutive interior angles
Part b) [tex](3x+4)\°+(2x+11)\°=180\°[/tex]
Part c) m∠5=[tex]77\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
Part a) Angles 3 and 5 are consecutive interior angles
therefore
m∠3+m∠5=[tex]180\°[/tex]
Part b) we have
m∠3=[tex](3x+4)\°[/tex]
m∠5=[tex](2x+11)\°[/tex]
substitute
[tex](3x+4)\°+(2x+11)\°=180\°[/tex]
Part c) solve for x
[tex](5x+15)\°=180\°[/tex]
[tex]5x=180\°-15\°[/tex]
[tex]x=180\°-15\°=33\°[/tex]
Find the value of m∠5
m∠5=[tex](2(33)+11)\°[/tex]
m∠5=[tex]77\°[/tex]
