Answer:
A: [tex]55[/tex]°
B: [tex]125[/tex]°
C: [tex]55[/tex]°
Step-by-step explanation:
Geometry properties!
When we look at this photo we see that [tex]a[/tex] and [tex]b[/tex] are on a line, meaning that [tex]a+b=180[/tex].
But because we don't have enough info yet we can't solve for them.
So let's head over to [tex]c[/tex].
For [tex]c[/tex] we see that it is also on a line with a right angle, and 35 degrees. This means that:
[tex]c + 90 + 35 = 180[/tex]
If we solve for [tex]c[/tex], we get:
[tex]c=180-90-35= 55[/tex].
Now we see that [tex]a[/tex] makes a vertical angle with [tex]c[/tex], meaning that angle [tex]a[/tex] is equal to angle [tex]c[/tex].
So now we know what angle [tex]a[/tex] is: [tex]55[/tex]°
Now we can go back to [tex]a + b =180[/tex]
Since we know [tex]a =55\\\text{we can get}\\55+b=180\\b=180-55=125[/tex]
That's it!
