Question

angle relationship review
supplementary angles, complementary angles, vertical angles, triangle angles
write and solve the equation to determine the value of the variable. then substitute this value into each expression
to determine the angle measurements. write the angle measurements inside the diagram. at the bottom of each
box provide the relationship of the angles: complementary, supplementary, vertical, or triangle sum theorem.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.

Explanation:

Step1: Analyze the relationship in problem 1

The two angles \(2x + 25\) and \(4x+35\) are supplementary (they form a straight - line). The sum of supplementary angles is \(180^{\circ}\). So, the equation is \((2x + 25)+(4x + 35)=180\).

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Step2: Analyze the relationship in problem 2

The two angles \(2x + 18\) and \(3x+2\) are complementary (they form a right - angle). The sum of complementary angles is \(90^{\circ}\). So, the equation is \((2x + 18)+(3x + 2)=90\).

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Step3: Analyze the relationship in problem 3

The two angles \(3x + 24\) and \(6x+18\) are vertical angles (opposite angles formed by two intersecting lines). Vertical angles are equal. So, the equation is \(3x + 24=6x+18\).

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Step4: Analyze the relationship in problem 4

The two angles \(4x + 88\) and \(14x+8\) are vertical angles. So, the equation is \(4x + 88=14x+8\).

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Step5: Analyze the relationship in problem 5

The two angles \(6x - 24\) and \(9x+24\) are vertical angles. So, the equation is \(6x - 24=9x+24\).

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Step6: Analyze the relationship in problem 6

The two angles \(12x + 28\) and \(3x+62\) are supplementary. So, the equation is \((12x + 28)+(3x + 62)=180\).

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Step7: Analyze the relationship in problem 7

The two angles \(6x - 12\) and \(4x+32\) are complementary. So, the equation is \((6x - 12)+(4x + 32)=90\).

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Step8: Analyze the relationship in problem 8

The two angles \(12x + 30\) and \(8x - 10\) are supplementary. So, the equation is \((12x + 30)+(8x - 10)=180\).

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Step9: Analyze the relationship in problem 9

The two angles \(7x + 32\) and \(13x - 12\) are supplementary. So, the equation is \((7x + 32)+(13x - 12)=180\).

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Step10: Analyze the relationship in problem 10

The two angles \(4x + 21\) and \(2x+9\) are complementary. So, the equation is \((4x + 21)+(2x + 9)=90\).

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Step11: Analyze the relationship in problem 11

The two angles \(4x + 18\) and \(2x+36\) are supplementary. So, the equation is \((4x + 18)+(2x + 36)=180\).

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Step12: Analyze the relationship in problem 12

The two angles \(3x + 27\) and \(2x+43\) are supplementary. So, the equation is \((3x + 27)+(2x + 43)=180\).

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Answer:

1. \(x = 20\) (Supplementary)
2. \(x = 14\) (Complementary)
3. \(x = 2\) (Vertical)
4. \(x = 8\) (Vertical)
5. \(x=-16\) (Vertical)
6. \(x = 6\) (Supplementary)
7. \(x = 7\) (Complementary)
8. \(x = 8\) (Supplementary)
9. \(x = 8\) (Supplementary)
10. \(x = 10\) (Complementary)
11. \(x = 21\) (Supplementary)
12. \(x = 22\) (Supplementary)