Answer:
a= 40, b= 50, c= 115
Step-by-step explanation:
a-
There is a theorem for a that gives you the answer:
Vertical angles are congruent
If the vertical angle of a is 40°, then a is also 40°.
That is what the theorem says.
b-
This one is kind of difficult, but let me break down the steps.
Now you already know that a is 40°, and the other angle besides b is a right angle because it shows a square, or 90°.
And now you need to know another law:
Every single triangle's angle adds up to 180°.
Now, this is basically a subtraction problem.
If two of the angles are there, and you know that all of the angles of a triangle add up to 180°, then you just need to know what 90 + 40 + x = 180 is
90 + 40 = 130
130 + x = 180
Subtract 130 from both sides
130 + x = 180
-130 -130
x=50, which means that all of the angles add up to 180°, or following the law.
c-
This one is different as well.
You can very clearly see that it is a straight line that crosses 65° and c.
There is one more law as well:
A straight line is 180°.
If that line that 65 degrees and c sits on is straight, that means that-
65 + x = 180, or
180 - 65 = x
180-65 = 115, and c=115.
It also follows that law; 115 + 65 = 180, which means that it is correct.
Hope this helps :)
-jp524
