Question

Find x in the following figure.
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Answer 1

For this question, you might want to apply "line and angle properties", specifically corresponding angles' properties.

First, you might notice that the line; AC, is originally supposed to be a transversal. So first, let's find out C, while angle A is known, if we are to keep in mind, AC as a transversal.

If you are assuming AC, as a transversal, note that angle C, and A, form corresponding angles. If you don't know what they area, I suggest, you consult this webpage; https://www.mathsisfun.com/definitions/corresponding-angles.html

Anyhow, corresponding angles, are angles, which are, upon a transversal, positioned in the same location, on the same side, on the same sector of the line they are upon (right/left, or up/down). So this property of theirs indicates that their angles would eventually be the same.

Meaning that if A, is 90, its corresponding angle; angle C, will eventually be the same, so we can conclude that C is 90 degree.

However, we have to find angle x. Here, an apparent property of x is that it composes one of the two parts of angle C. Its actually been cut out, you can say, so we can solve these properties, to form an "equation", to find out angle x, or "unknown angle's value". Hence,

C=90 degree

First part of C= 40 degree

Second part of C= x degrees

C= First part + second part (unknown: x)

90=40+x

90-40=x

50=x

So, the unknown angle, or angle x, is equal to: 50 degrees, since it adds up to 40 degrees, to form C, or 90 degrees.