Answer:
Part 5) [tex]x=50\°[/tex]
Part 6) [tex]x=15\°[/tex]
Step-by-step explanation:
Part 5) we know that
[tex](2x-10)\°+90\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)
solve for x
[tex]2x=180\°-80\°[/tex]
[tex]2x=100\°[/tex]
[tex]x=50\°[/tex]
Find the value of the labeled angle
[tex](2x-10)\°=2(50\°)-10\°=90\°[/tex] ----> is a right angle
Verify the answer
we know that
In a quadrilateral the sum of the internal angles must be equal to 360 degrees
so
[tex](2x-10)\°+90\°+(180-x)\°+x\°=360\°[/tex]
[tex](2x+260)\°=360\°[/tex]
substitute the value of x
[tex]2(50\°)+260\°=360\°[/tex]
[tex]360\°=360\°[/tex] ------> is true, therefore the value of x is correct
Part 6) we know that
[tex](8x+10)\°+(4x-10)\°=180\°[/tex] -----> by consecutive interior angles (supplementary angles)
solve for x
[tex]12x=180\°[/tex]
[tex]x=15\°[/tex]
Find the value of each labeled angle
[tex](8x+10)\°=8(15\°)+10\°=130\°[/tex]
[tex](4x-10)\°=4(15\°)-10\°=50\°[/tex]
[tex]130\°[/tex] and [tex]50\°[/tex] are supplementary angles
