At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I can't see how one can figure out those angles without some other properties of the lines. For example, angle 4 could be 90 degrees if P is center and line HD is a tangent to circle. But, that is not "given" by just looking at the picture.
Find the measure of the following numbered angles in circle P when arc AE = 53°, arc BA= 68°, and arc CB = 72°.
Angle 7 = arc AB + arc AE = 53 + 68 = 131 degrees. Triangle PBE = isosceles triangle => angle 3 = (180-angle7)/2 Keep going like that.
would angle 8 be 90?
No. You need to calculate based on arc and triangle properties.
well, since BA=68, wouldn't angle 1 be half?
No. Angle 1 can be only obtained after you figure out: 1) Angle 4 2) Angle 2 3) Angle 6 in that order.
Angle 4 is 90 degrees if line HD looks like a tangent. It appears more information is needed. Also, it is nearly impossible to keep referring to the image in a different browser window and rationally respond.
I know angle 4=90 so wouldn't angle 2=45?
Yeah, I know. I don't know any other way to post the problem.
Angle 2 is greater than angle 4. So, it must be 90 plus something. To get that something, you need to form triangle PBA first. It will be an isosceles triangle. Given arc BA = 68 degrees, angles A and B in that triangle PBA = (180-68)/2 = 59 degrees. Angle B in that triangle PBA = angle 3 + angle ABF. Because you know angle 3 and angle PBA, you can get angle ABF. From that, you use the fact that triangle BAD forms right triangle to find angle ADB. You add 90 degrees to that to get angle 2. Very complex. :)
wow, I'll have to work on that, thanks!