Questions: Calculator For what value of (x) is line a parallel to line (b) ? Enter your answer in the box. (x=)

Calculator For what value of (x) is line a parallel to line (b) ? Enter your answer in the box. (x=)
Transcript text: Calculator For what value of $x$ is line a parallel to line $b$ ? Enter your answer in the box. \[ x= \] $\square$
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Solution

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Solution Steps

Step 1: Find the angle supplementary to 116°

The angle adjacent to 116° and below line _b_ sums to 180° with it. 180° - 116° = 64°. This confirms the given angle of 64°.

Step 2: Find the other angle supplementary to 64°

The angle adjacent to 64° below line _b_ also sums to 180° with it. This angle is also adjacent to the angle (4x + 28)° forming a pair of corresponding angles. 180° - 64° = 116°.

Step 3: Set up an equation

If lines _a_ and _b_ are parallel, corresponding angles are congruent. Set (4x + 28) equal to 116 and solve for _x_.

Step 4: Solve for _x_

4x + 28 = 116 4x = 88 x = 22

Final Answer:

x = 22

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