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2 years ago

the exterior angle of a regular polygon is one third the size of its interior angle. how many sides does the polygon have

Mathematics

1 answer:

Aloiza [94]2 years ago

7 0

Answer:

8 sides

Step-by-step explanation:

let x be the exterior angle then 3x is the interior angle

interior angle + exterior angle = 180° , then

x + 3x = 180

4x = 180 ( divide both sides by 4 )

x = 45

the sum of the exterior angles of a polygon = 360°

since the polygon is regular with each exterior angle = 45°, then

number of sides = 360° ÷ 45° = 8

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Read 2 more answers

CD is perpendicular to AB and passes through point C5, 12).

Aleksandr-060686 [28]

Answer:

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Step-by-step explanation:

We are given a line AB with its end coordinates. and Another line segment CD which is perpendicular to AB. We have the coordinates of C , and we are asked to find the x intercept of line CD.

For that we need to find the equation of CD

we have coordinates of C , and hence if we have slope of CD we can find equation of CD

Slope of CD can be determine with the help of slope of AB as CD⊥ AB

So, the slope of CD $mCD = -\frac{1}{mAB}$

Hence we start from determining slope of AB

slope is given as

$m= \frac{y_2-y_1}{x_2-x_1}$

$m= \frac{14-(-3)}{7-(-10)}=\frac{17}{17}=1$

Hence $mAB=1$

There fore $mCD=-1$

(∵ Product of Slopes of two perpendicular lines is always -1)

Now we find the equation of CD with the help of slope -1 and coordinates of C(5,12)

$m=\frac{y-y_1}{x-x_1}$

$-1=\frac{y-12}{x-5}$

$-x+5=y-12$

$y=-x+17$

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$0=-x+17$

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2 years ago

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lorasvet [3.4K]

Answer: -437

Step-by-step explanation:

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3 years ago