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

Video Transcript

Given that lines 𝐴𝐵 and 𝐶𝐷 intersect at 𝑂, find the measurement of angle 𝐴𝑂𝐶.

Angle 𝐴𝑂𝐶 is marked with the orange line. We know that angle 𝐴𝑂𝐶 is equal to angle 𝐵𝑂𝐷 because these angles are opposite and opposite angles are equal. But the measurement of angle 𝐵𝑂𝐷 is not given. It’s been split into two angles: one measures 35 degrees and the other measures 48.

So to find the measurements of angle 𝐵𝑂𝐷 and angle 𝐴𝑂𝐶, we need to add together 48 and 35. Eight and five is 13. Four and three plus the one we exchanged gives us a total of eight. 48 plus 35 is 83.

So the measurement of angle 𝐴𝑂𝐶 is 83 degrees.