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aleksandrvk [35]

3 years ago

10

Find the measures of an interior angle and an exterior angle of a regular hexagon. The measure of an interior angle is 120. The

measure of an exterior angle is PLS HELP I NEED THIS ASAP
Find the sum of the angle measures of a hexagon.
The sum is
______________ degrees.

1 answer:

Tom [10]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

Since a hexagon has 6 interior angles and the measure of one is 120°, then

sum of interior angles = 6 × 120° = 720°

exterior angle = 180° - interior angle = 180° - 120° = 60°

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If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

$cos(\alpha)=-\frac{8}{17}$

Find the value of sine

$cos^{2} (\alpha)+sin^2(\alpha)=1$

substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

$cos^{2} (\beta)+sin^2(\beta)=1$

substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

$cos^2(\beta)=1-\frac{16}{25}$

$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

$sin(\beta)=-\frac{4}{5}$

$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

4 0

3 years ago

When Derek planted a tree it was 36 inches tall. The tree grew 1 1/4 inches per year. The tree is now 44 3/4 inches tall. How ma

Tcecarenko [31]

148

Step-by-step explanation:

44 3/4 : 11/4 =?

if you do this you will find the solution =>years

6 0

3 years ago

Read 2 more answers

Which is the value of i^20+1?

Nonamiya [84]

Answer:

Step-by-step explanation:

$i^{20}+1=i^{2*10}+1\\\\(i^{2})^{10}+1=(-1)^{10}+1\\\\=1+1=2$

8 0

3 years ago

Can someone help please and thank you!

kondor19780726 [428]

Answer:

10 and 40 I think maybe?

Step-by-step explanation:

I hope this is correct if not I am so so so so so so sorry

5 0

3 years ago

Read 2 more answers

Vladimir [108]

Answer:

5.5 inches

Step-by-step explanation:

1) the formula to find the area of a square is l^2= area and l=length

in this case we already know the area but not the length

so we have to find the square root of 30 as the opposite operation needs to be used to find the missing number

so

√30= 5.47

5.47 rounded= 5.5

the length of one side is 5.5 in

5 0

3 years ago