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mr_godi [17]
3 years ago
7

Determine the measure of an interior angle of the named regular polygon. If a side of the polygon is extended, determine the sup

plemntsry angle of an interior angle.
A) the measure of each interior angle of a regular hexagon is

B) the measure of the supplementary angle of an interior angle is
Mathematics
1 answer:
ladessa [460]3 years ago
6 0

Answer:

A) Each interior angle of the Regular Hexagon = 120°

B)The measure of the supplementary angle of an interior angle is  60°

Step-by-step explanation:

Regular Hexagon : A 6 sided polygon which has all 6 interior angles as  EQUAL is called a regular hexagon.

So, here are 6 interior angles of the hexagon are equal.

Also, Sum of all interior angles of an hexagon = 720°

Let us assume the each angle of the hexagon = m

⇒ m + m + m + m + m  + m = 720°

or, 6 m = 720°

or, m = 720° / 6 = 120°

⇒ Each interior angle of the Regular Hexagon = 120°

Now, a side is extended to form an exterior angle.

Let us assume the measure of that exterior angle  = k

⇒ k + m = 180 °   ( as k and m are SUPPLEMENTARY ANGLES)

or,  k = 180 - 120   = 60 °

or, k = 60 °

Hence,  the measure of the supplementary angle of an interior angle is  60°

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Given: y // z Prove: measure of angle 5 plus measure of angle 2 plus measure of angle 6 equals 180 degrees
lilavasa [31]

Step-by-step explanation:

Given: y // z Prove: measure of angle 5 plus measure of angle 2 plus measure of angle 6 equals 180 degrees

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21. Name an angle that is adjacent to O ZDGB<br> O ZEGC<br> O ZEGF<br> O ZCGB<br> O ZFGA<br> O ZEGT<br> O ZDGE
olga2289 [7]

Answer:

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6 0
3 years ago
NO LINKS!!
dexar [7]

Answer: Anything between 0 and 10, excluding both endpoints.

In terms of symbols we can say 0 < w < 10 where w is the width.

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

Explanation:

You could do this with two variables, but I think it's easier to instead use one variable only. This is because the length is dependent on what you pick for the width.

w = width

2w = twice the width

2w-5 = five less than twice the width = length

So,

  • width = w
  • length = 2w-5

which lead to

area = length*width

area = (2w-5)*w

area = 2w^2-5w

area < 150

2w^2 - 5w < 150

2w^2 - 5w - 150 < 0

To solve this inequality, we will solve the equation 2w^2-5w-150 = 0

Use the quadratic formula. Plug in a = 2, b = -5, c = -150

w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-150)}}{2(2)}\\\\w = \frac{5\pm\sqrt{1225}}{4}\\\\w = \frac{5\pm35}{4}\\\\w = \frac{5+35}{4} \ \text{ or } \ w = \frac{5-35}{4}\\\\w = \frac{40}{4} \ \text{ or } \ w = \frac{-30}{4}\\\\w = 10 \ \text{ or } \ w = -7.5\\\\

Ignore the negative solution as it makes no sense to have a negative width.

The only practical root is w = 10.

If w = 10 feet, then the area = 2w^2-5w results in 150 square feet.

----------------------

Based on that root, we need to try a sample value that is to the left of it.

Let's say we try w = 5.

2w^2 - 5w < 150

2*5^2 - 5*5 < 150

25 < 150 ... which is true

This shows that if 0 < w < 10, then 2w^2-5w < 150 is true.

Now try something to the right of 10. I'll pick w = 15

2w^2 - 5w < 150

2*15^2 - 5*15 < 150

375 < 150 ... which is false

It means w > 10 leads to 2w^2-5w < 150  being false.

Therefore w > 10 isn't allowed if we want 2w^2-5w < 150 to be true.

4 0
2 years ago
Can someone please help me?
denis-greek [22]

Answer:

B

Step-by-step explanation:

Use a graphing calculator like desmos and youll find the answer

3 0
2 years ago
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