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Answer:
See below:
Step-by-step explanation:
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Theorums
To solve the problem, since it is in the field of Geometry, there is bound to be theorums and basic knowledge that we need to know, upon seeing this problem what we need to know are:
Supplementary Angles: When two angles add up to 180 degrees.
Complementary Angles: When two angles add up to 90 degrees.
Interior/Exterior Angles Theorum.
Right Angles.
Solving
So to solve this, I'll first start with number 11. In this, we need to solve for B and we are given the first angle and b as the second angle.
What we can do is first we know that it is a Complementary angle as we know 65 degrees + b has to equal to 90 degrees.
Upon solving that, we know that B for the first one is
We know that b is 25 degrees for the first one.
For the second one, we know that due to the interior/exterior angles theorem that 80 + b has to equal to 180 degrees due to the int/ext angles theorem and supplementary angles.
We know that b is 100 degrees.
For the third one, we know the entire thing is 360 degrees. Since we know that, we can solve for b as we have all the angles needed.
Upon solving, we know that b is 93 degrees.
For the final one, due to vertical angles, b is equal to 48 degrees!
Feel free to ask any questions you have in the comments!
Cheers!