Video Transcript
In the given figure, find the
measure of angle 𝑃𝐶𝑄.
Observe that angle 𝐶𝐴𝐵 is
vertically opposite angle 𝑀𝐴𝐿. This means that the two angles are
congruent. Similarly, angle 𝐴𝐵𝐶 is
vertically opposite and, therefore, congruent to angle 𝑂𝐵𝑁. Since 𝐴𝐵𝐶 is a triangle, we know
that its internal angles sum to 180 degrees.
The internal angles of triangle
𝐴𝐵𝐶 are angles 𝐶𝐴𝐵, 𝐴𝐵𝐶, and 𝐵𝐶𝐴. Therefore, angle 𝐵𝐶𝐴 has measure
180 minus 80 minus 30 equals 70 degrees. Finally, since angle 𝑃𝐶𝑄 is
vertically opposite angle 𝐵𝐶𝐴, the two angles are congruent. Therefore, angle 𝑃𝐶𝑄 has measure
70 degrees.
