Problem 1
Answer: Choice B) angle1 = 26, angle2 = 64
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Explanation:
Complementary angles add to 90
(angle1)+(angle2) = 90
(5x+6)+(68-x) = 90
4x+74 = 90
4x = 90-74
4x = 16
x = 16/4
x = 4
So,
angle1 = 5x+6 = 5(4)+6 = 26
angle2 = 68-x = 68-4 = 64
Note how
angle1+angle2 = 26+64 = 90
to help check our answer
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Problem 2
Answer: Choice D) BC, AC, AB
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Explanation:
The shortest side of a triangle is always opposite the smallest angle.
The longest side of a triangle is always opposite the largest angle.
Based on those two facts, we can say the shortest side is BC (since angle A = 53 is the smallest angle) and the longest side is AB (since angle C = 70 is the largest)
The order from smallest to largest is
BC, AC, AB
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Problem 3
Answer: Choice D) B < C < A
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Explanation:
Use the reverse of the idea from problem 2. We know that AC is the smallest side which must mean that angle B is the smallest angle. Since BC is the largest side, angle A must be the largest angle.
The order of the angles is B < C < A
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Problem 4
Answer: Choice A) angle 5 = 50, angle 8 = 130
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Explanation:
The same side exterior angles must be supplementary to have parallel lines.
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Problem 5
Answer: Choice A) angle G is the smallest
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Explanation:
Use the same idea as problem 2. The smallest angle is opposite the smallest side. The smallest side is 48, so angle G being opposite of that side, is the smallest angle.
Angle O would be the largest as it is opposite the largest side DG = 70
