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Bethani Gasparine

Work out the value of 𝑥 in the figure.

𝑥 is an angle that’s measured in degrees, and there’s another angle that measures 131 degrees. We have a set of parallel lines that are cut by a transversal. This means the angle that’s 131 degrees is going to be equal to another angle that is supplementary to 𝑥.

We know the angles measuring 131 degrees are equal because they are alternate exterior angles; they’re on alternate sides of the transversal and on the exterior of the parallel lines.

So these two angles should add to 180 degrees because they form a linear pair; they create a line, which is 180 degrees; they are supplementary. Therefore, we can say 131 plus 𝑥 equals 180 because these two angles added together will combine to equal 180 degrees.

So to solve for 𝑥, we need to subtract both sides by 131. And we get that 𝑥 is equal to 49. Therefore, the value of 𝑥 in our figure is 49 degrees.

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