Problem 1)
This question is incomplete. It asks us to find something, but doesn't say what to find. It's literally blank after the word "find" which suggests your teacher made a typo. Please get back to me on this. Thanks.
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Problem 2)
Angles GAR and GAT are supplementary because they are a linear pair. They form a straight angle. So we add up the expressions of x for each of these angles, solve for x, and use this to find angle GAR.
(angle GAR) + (angle GAT) = 180
(5x) + (3x+4) = 180
8x+4 = 180
8x+4-4 = 180-4
8x = 176
8x/8 = 176/8
x = 22
Note: now that I reached this point I realize that this might be the answer to problem 1; however, I'm not 100% sure because of the incomplete problem.
Use this x value to find angle GAR
angle GAR = 5*x
angle GAR = 5*22
angle GAR = 110
Unfortunately this answer isn't listed. I'm thinking your teacher made another typo.
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Problem 3)
Answer: angle GAR and angle ABQ are corresponding angles.
Thankfully this answer is listed. Corresponding angles are angles that are on the same side of the transversal line and they are either both above or below the parallel lines they are next to. In this case, they are both above the parallel line counerparts.
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Problem 4)
Corresponding angles are congruent as long as we have a set of parallel lines. So that means angle ABQ is equal to angle GAR. So angle ABQ is also 110 degrees
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Problem 5)
angle BAT = angle GAR, because they are vertical angles
angle BAT = 110
angle BAT = (angle BAD) + (angle DAT)
(angle BAD) + (angle DAT) = angle BAT
(100) + (angle DAT) = 110
angle DAT = 110-100
angle DAT = 10
angle ADB = angle DAT, because they are alternate interior angles
angle ADB = 10
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Final Answer: 10 degrees
is 0.2222222222 and so on
is 0.4444444444 and so on
is 0.777777777 and so on
