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stepladder [879]
3 years ago
7

Find the measure indicated. Assume that the lines which appear to be tangent are tangent. Part 4

Mathematics
2 answers:
ella [17]3 years ago
8 0

The angle between the two tangents drawn from an external point to a circle and the angle subtended by the line segment joining the points of the contact at the Centre are supplymentary,

So,

15.) let the unknown angle be x

=》x + 55° = 180°

=》x = 180° - 55°

=》

\boxed{x = 125°}

16. let the unknown angle be n

=》n + 80° = 180°

=》n = 180° - 80°

=》

\boxed{n = 100°}

Klio2033 [76]3 years ago
6 0

9514 1404 393

Answer:

  15)  125°

  16  100°

Step-by-step explanation:

The short arc where two tangents intersect a circle, and the angle where the tangents meet are supplementary.

__

15) ? = 180° -55° = 125°

16) ? = 180° - 80° = 100°

_____

<em>Additional comment</em>

The quadrilateral formed by the tangents and the radii to the points of tangency has a total interior angle measure of 360°. The angles where the radii meet the tangents are 90°, so the sum of the external angle and the central angle is 360° -90° -90° = 180°. That is, the external angle and the central angle are supplementary.

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aliina [53]
300 jelly beans cost you x dollars.
if you divide 300 by x, you get the number of jelly beans per dollar.
now you are buying 1/2 a dollar's worth of jelly beans, so you will be getting 1/2 * 300 / x which is equal to 150 / x jelly beans.
the actual number of jelly beans you get is determined by x.
if x = 1, the you get 150 jelly beans for 1/2 of a dollar.
if x = 3, then you get 50 jelly beans for 1/2 of a dollar.

you can also work this out by determing the cost per jelly bean.
if you pay x dollars for 300 jelly beans, then the cost per jelly bean is equal to x/300.
now you want to buy 50 cents worth of jelly beans.
the number of jelly beans you can buy is the money you pay divided by the cost per jelly bean.
you pay 50 cents which is equal to 1/2 of a dollar.
you will get 1/2 / (x/300) which is equal to ((1/2)*300)/x which is equal to 150/x.
now let's assume x is equal to 1.
you will get 150/1 = 150 jelly beans.
now let's assume x is equal to 3.
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the equation becomes:
number of jelly beans = 150/x
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it's just a matter of how you want to look at it.

another way to look at it would be to set up a ratio.
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simplify to get:
150 = x*y
divide both sides of the equation by x to get:
y = 150/x
same equation again.
x is the cost for 300 jelly beans.
y is the number of jelly beans you can get for half a dollar.
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