Question

identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutive interior, vertical, or supplementary. find the value of x and the measure of each angle.
1)
2)
3)
4)

Explanation:

Step1: Analyze the relationship between angles in problem 1

The angles \(25x + 4\) and \(26x-1\) are supplementary (their sum is \(180^{\circ}\)).

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\(\angle1=25x + 4=25\times3.47+4 = 86.75+4=90.75^{\circ}\)
\(\angle2=26x-1=26\times3.47-1=90.22 - 1=89.22^{\circ}\)

Step2: Analyze the relationship between angles in problem 2

The angles \(6x + 8\) and \(19x-3\) are supplementary (their sum is \(180^{\circ}\)).

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\(\angle1=6x + 8=6\times7+8=42 + 8=50^{\circ}\)
\(\angle2=19x-3=19\times7-3=133 - 3=130^{\circ}\)

Step3: Analyze the relationship between angles in problem 3

The angles \(12x + 12\) and \(14x-6\) are supplementary (their sum is \(180^{\circ}\)).

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\(\angle1=12x + 12=12\times6.69+12=80.28+12=92.28^{\circ}\)
\(\angle2=14x-6=14\times6.69-6=93.66 - 6=87.66^{\circ}\)

Step4: Analyze the relationship between angles in problem 4

The angles \(32x + 4\) and \(33x+1\) are supplementary (their sum is \(180^{\circ}\)).

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\(\angle1=32x + 4=32\times\frac{35}{13}+4=\frac{1120}{13}+4=\frac{1120 + 52}{13}=\frac{1172}{13}\approx90.15^{\circ}\)
\(\angle2=33x+1=33\times\frac{35}{13}+1=\frac{1155}{13}+1=\frac{1155+13}{13}=\frac{1168}{13}\approx89.85^{\circ}\)

Answer:

1. \(x = 3.47\), \(\angle1 = 90.75^{\circ}\), \(\angle2=89.22^{\circ}\)
2. \(x = 7\), \(\angle1 = 50^{\circ}\), \(\angle2=130^{\circ}\)
3. \(x = 6.69\), \(\angle1 = 92.28^{\circ}\), \(\angle2=87.66^{\circ}\)
4. \(x=\frac{35}{13}\approx2.69\), \(\angle1\approx90.15^{\circ}\), \(\angle2\approx89.85^{\circ}\)