Find the measure of angle
Let’s have a closer look at the
figure we’ve been given. There is a triangle formed by
connecting the points 𝐴, 𝐵, and 𝐶. The measure of one of the interior
angles in this triangle, angle 𝐴𝐵𝐶, has been marked as 35 degrees. And the measure of the angle we’ve
been asked to calculate, angle 𝐴𝐶𝐵, has been marked as 𝑥. We’re also given the measure of an
angle outside the triangle, which is 65 degrees. The final thing to note is that
line 𝐵𝐴 and line 𝐶𝐷, as we’ve now labeled it, are parallel, as indicated by the
arrows along their lengths.
Now, we need to consider how we can
use all this information to determine the measure of angle 𝐴𝐶𝐵. Because lines 𝐵𝐴 and 𝐶𝐷 are
parallel, angle 𝐴𝐶𝐷 and angle 𝐶𝐴𝐵 are alternate angles. Alternate angles are of equal
measure, so this tells us that the measure of angle 𝐶𝐴𝐵 is also 65 degrees.
We now know the measures of two of
the interior angles in triangle 𝐴𝐵𝐶, and we wish to calculate the measure of the
third. We can recall that the sum of the
measures of the interior angles in any triangle is 180 degrees. We can therefore form an equation
using the measures of the interior angles of triangle 𝐴𝐵𝐶. 𝑥 plus 35 degrees plus 65 degrees
equals 180 degrees. This equation simplifies to 𝑥 plus
100 degrees equals 180 degrees. 𝑥 is therefore equal to 180
degrees minus 100 degrees, which is 80 degrees.
Remember 𝑥 represents the measure
of angle 𝐴𝐶𝐵. So using the sum of the measures of
the interior angles in a triangle, we found that the measure of angle 𝐴𝐶𝐵 is 80