Find the measure of the arc or angle indicated assume that lines which appear tangent are tangent

Video Transcript

We want to find the measure of the arc or angle- that's indicated, assuming that lines when, if your tangent arc tangent, so we want to find the measure of the arc and number 7 knowing that this angle is 40 degrees. That is at the point of tangency, which means that the amount of arc is going to be twice that it's 80 degrees of arc and circles have 360 degrees. If we know 80 of it, the rest is 280 pot. If we have an arc of 238 degrees, then 360 minus 238 would leave 122 point, but then the angle that opens up to it to that intercepted arc would be half of 122 and half of 12261 degrees in number 9. An angle that is inside of the circle is equal to half of the sum of the intercepted arcs the 1. It directly opens up to 99 degrees and the 1 on its vertical side, behind it, 55 degrees and so 1 half of 99 plus 55 is 77 degrees. Poi again, the angle is equal to half of the 2. The sum of the 2 arcs so i'll call 1 of them x for the unknown and 62 point. So we would. We could multiply both sides by 276 times. 2 is 152, and that would equal x, plus 62 and then subtract 62 to both sides. 152. Minus 62 is 90 degrees.

How do you find the tangent measure?