Answer:
a. [tex]x=81\°[/tex]
b. [tex]y=99\°[/tex]
c. [tex]z=129\°[/tex]
Step-by-step explanation:
a. By definition, the sum of the interior angles of a triangle is 180 degrees.
Then you know that:
[tex]51\°+48\°+x=180\°[/tex]
Solving for "x", you get:
[tex]x=180\°-51\°-48\°\\\\x=81\°[/tex]
b. Notice the angle "x" and the "y" form and straight angle (180°), then they are supplementary, which means that their sum is 180°. Then:
[tex]x+y=180\°[/tex]
Substituting the value of "x" into the equation and solving for "y", you get:
[tex]81\°+y=180\°\\\\y=180\°-81\°\\\\y=99\°[/tex]
c. The angle that measures 51° and the angle "z" form and straight angle, then they are supplementary. This means that:
[tex]51\°+z=180\°[/tex]
Solving for "z", you get:
[tex]z=180\°-51\°\\\\z=129\°[/tex]
