Problem 11
Answers:
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Explanation:
The two angles shown here form a linear pair. They supplementary so they add to 180.
(5x+20)+(3x-8) = 180
(5x+3x) + (20-8) = 180
8x+12 = 180
8x = 180-12
8x = 168
x = 168/8
x = 21
We then find the angles to be
5x+20 = 5*21+20 = 125
3x-8 = 3*21-8 = 55
Note how 125+55 = 180 to help confirm the answers
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Problem 12
Answer: B) Vertical angles
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Explanation:
Vertical angles are angles that form after intersecting two lines, and the angles are opposite one another. So one example of a vertical angle pairing would be angles 1 and 3. The other vertical angle pair of this diagram are angles 2 and 4. Vertical angles are always congruent to one another.
In this diagram, angles 1 and 4 are adjacent since they are next to each other. In other words, they share a common line (think of apartment neighbors sharing a common wall). Since they are adjacent angles, there is no way they are vertical angles.
Angles 1 and 4 are also supplementary since they form a straight line. They are a linear pair for very similar reasons. This allows us to rule out choices A, C and D.
Side note: the term "linear pair" means that the angles are adjacent and supplementary.
