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Video: Finding the Measure of an Angle Using the Properties of Vertically Opposite Angles

Tim Burnham

Find the value of 𝑥.

02:02

Video Transcript

Find the value of 𝑥.

Well 𝑥 is the number of degrees in the measure of this angle here. Now in our diagram, we’ve got two intersecting lines, 𝐴𝐶 and 𝐵𝐷. And when you have straight lines that cross over like that, the opposite angles, vertically opposite angles in fact, are equal. So the measure of those two angles is equal, and the measure of those two angles are equal. So vertically opposite angles are equal in measure.

Now this means that a hundred and forty-four degrees is equal to seventy-four degrees plus 𝑥 degrees. And we can write out the equation: a hundred and forty-four equals seventy-four plus 𝑥.

Now if I take away seventy-four from the left-hand side and I take away seventy-four from the right-hand side, then on the right-hand side seventy-four take away seventy-four is nothing, so that just leaves me with 𝑥, and on the left-hand side a hundred and forty-four minus seventy-four is seventy.

So the answer is 𝑥 is equal to seventy. And just before we finish, here’s a question. Is 𝑥 equals seventy degrees a correct answer?

Well if we look carefully at the diagram, 𝑥 is the number of degrees; there’s a degree symbol above it there. And that means if we said 𝑥 was equal to seventy degrees, we’ll be saying that the measure of this angle here is seventy degrees degrees, and that would be wrong.

So technically, 𝑥 equals seventy degrees is not a correct answer. You’d probably get one mark or half a mark. But if we want to be absolutely mathematically correct, the answer has to be 𝑥 is equal to just the number seventy.