So, we have a diagram and we’re
asked to find the measure of angle 𝐵𝐴𝐶. So, that means the angle formed
when we move from 𝐵 to 𝐴 to 𝐶, so it’s this angle here.
So, that’s the angle we’re looking
to find. But we can’t work it out
straightaway because we only currently know one of the angles in the triangle. We can, however, work out what the
other angle in the triangle is, so angle 𝐵𝐶𝐴. Because what you’ll notice is that
angle 𝐵𝐶𝐴 is on a straight line with this angle of 163 degrees.
So, we can use that fact about
angles on a straight line, to work out angle 𝐵𝐶𝐴 first. So, the measure of angle 𝐵𝐶𝐴 is
180 minus 163, and that gives us 17 degrees. And the reasoning for that, which
I’ve written at the side, is that angles on a straight line sum to 180 degrees. So, I can mark angle 𝐵𝐶𝐴 on to
the diagram. And there it is.
Now, we have enough information to
work out this angle 𝐵𝐴𝐶 that I was originally asked for because, again, we know
the angles in a triangle sum to 180 degrees. And if I know two of them, I can
work out the third. So, to find angle 𝐵𝐴𝐶, we’re
gonna do 180 minus 100 minus 17. That’s subtracting both of the
other two angles in the triangle. And so, that gives us 63 degrees
for the measure of angle 𝐵𝐴𝐶. And the reasoning, as we said,
angles in a triangle sum to 180 degrees.
So, often in questions like these,
you can’t work out the angle you’re looking for immediately. You may have to work out other
angles in the diagram first, by using facts about angles in a triangle or angles on
a straight line. And once you’ve got those, you can
then work out the angle you’re looking for.