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3 years ago

I need help on this please

Mathematics

2 answers:

Nimfa-mama [501]3 years ago

8 0

Since these equations are consecutive interior angles, they will add up to 180.
The equation will be (x+20)°+(4x-5)°=180.

(x+20)+(4x-5)=180
5x+15=180
5x=165
165/5x
=33°

You can make sure your answer is correct by putting your x back into the equation.
(33+20)+(4•33-5)
53+132-5
53+127
180

harina [27]3 years ago

6 0

Answer:

25/3

Step-by-step explanation:

Set the equations equal to each other since the lines are parallel.

(x+20)=(4x-5)

-x +5 -x +5

25/3 = 3x/3

x = 25/3

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1 year ago

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20.) A=49.23 degrees, c=54.8Solve the right triangle. Express angles in decimal degrees.

vivado [14]

$\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\ \end{gathered}$

Explanation

Step 1

a) let

$\begin{gathered} A=49.23\text{ \degree} \\ c=54.8\text{ \degree} \end{gathered}$

b) b value

to find the measure of side b we can use cosine function

$\begin{gathered} cos\theta=\frac{adjacent\text{ side}}{hypotenuse} \\ replace \\ cos\text{ 49.23=}\frac{b}{54.8} \\ b=54.8*cos49.23 \\ b=35.78 \end{gathered}$

c) angle B

to find the measure of Angle B we can use sine function

$\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ replace \\ sin\text{ B=}\frac{35.78}{54.8} \\ sin\text{ B= 0.65}\Rightarrow inverse\text{ function to isolate B} \\ B=\sin^{-1}(0.65) \\ B=40.76 \end{gathered}$

d) side a

$\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ sin\text{ A=}\frac{a}{c}=\frac{\placeholder{⬚}}{\placeholder{⬚}} \\ sin\text{ 49.23=}\frac{a}{54.8} \\ multiply\text{ both sides by 54.8} \\ 54.8s\imaginaryI n\text{49.23=}\frac{a}{54.8}*54.8 \\ 41.50=a \end{gathered}$

so, the answer is

$\begin{gathered} a=41.50 \\ b=35.78 \\ B=40.76\text{ \degree} \\ \end{gathered}$

I hope this helps you

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1 year ago