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IRINA_888 [86]
3 years ago
8

Parallel lines are cut by a transversal such that the alternate interior angles have measures of 3x + 17 and x + 53 degrees. The

value of x is:
A. 9
B. 18
C. 35
D. 71
Mathematics
1 answer:
Dvinal [7]3 years ago
8 0
Alternate interior angles are congruent...they are equal. So lets set them equal and solve for x

3x + 17 = x + 53
3x - x = 53 - 17
2x = 36
x = 36/2
x = 18

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Read 2 more answers
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aev [14]

Answer:

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Solving both inequalities one by one

\frac{2x+4}{3} \geq -17.5\\2x+4 \geq -52.5\\2x \geq -52.5-4\\2x \geq -56.5\\\frac{2x}{2} \geq \frac{-56.5}{2}\\x \geq -28.25\\\frac{2x+4}{3} < 17.5\\2x+4 < 52.5\\2x < 52.5-4\\2x \geq 48.5\\\frac{2x}{2} \geq \frac{48.5}{2}\\x < 24.25

The solution is:

-28.25 ≤ x < 24.25

We have to see which options lie in the solution range.

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