What's the fastest way to do these math problems?

jamesford
Thu, 30 Jul 2009 21:16:04 +0000

Thanks for all the help so far.

ImageShack - Best place for all of your image hosting and image sharing needs;

If x = 20 and y = 30 in the figure above, what is the value of z?

The figure is a quadrilateral, whose interior angles add up to 360.
360 - y - 2x gives us the fourth, obtuse angle
360 - 30 - 2(20)
= 290

The obtuse angle and z form a complete “revolution,” so 290 + z = 360 and z = 70

===============================

ImageShack - Best place for all of your image hosting and image sharing needs;

Point O is the center of both circles in the figure above. If the circumference of the large circle is 36 and the radius of the small circle is half the radius of the large circle, what is the length of the darkened arc?

While doing this timed I did the long way, finding big radius and then small radius and small circumference, then determining that the arc darkened is 80/360 of the total circumference.

Another method I figured out: the circumference of the circle is directly proportional to the radius of the circle. If the large circumference is 36 and its radius is twice that of the small circle, then the small circumference is 36/2 = 18. Then 80/360 = x/18 and x = 4.