Video Transcript
In the following figure, find the
value of 𝑥.
In the diagram, we have two
intersecting lines. These two angles here, we say, are
vertically opposite angles. And so, we recall what we know
about vertically opposite angles. We know that they’re equal. We say vertically opposite angles
are equal. And so, this means our two angles,
two 𝑥 plus five and 67, must be equal to one another. We write this as an equation: two
𝑥 plus five equals 67.
And we can solve this equation to
find the value of 𝑥 by performing a series of inverse operations. We begin by subtracting five from
both sides. When we subtract five from the
left-hand side, we’re left with two 𝑥. And 67 minus five is 62. So, our equation is now two 𝑥
equals 62. Currently, the 𝑥 is being
multiplied by two. And the inverse operation here then
is to divide through by two. Two 𝑥 divided by two is 𝑥. And 62 divided by two is 31. So, we’ve calculated 𝑥 to be equal
to 31.
Now, since we’ve worked with
algebra, it’s sensible to check our answer by substituting it back into the original
expression. Two 𝑥 means two times 𝑥. And we found 𝑥 to be 31. So, we multiply 31 by two and add
five. That’s 62 plus five, which is equal
to 67. We know that this must be equal to
67 since vertically opposite angles are equal. So, that’s an indication to us that
we’ve performed our calculations correctly. 𝑥 is equal to 31.
