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2 years ago

Find the value of x in each case:

Mathematics

2 answers:

Zanzabum2 years ago

6 0

Answer:

$x=30\°$

Step-by-step explanation:

Find the measures of interior angles in each triangle

Triangle BGC

$m$

The measures of triangle BGC are $90\°-60\°-30\°$

Triangle CGH

we know that

$m$ -----> by consecutive interior angles

we have that

$m$

substitute

$m$

we have

$m$

remember that

$m$

$60\°+2x+180\°-4x=180\°$

$60\°=2x$

$x=30\°$

The measures of triangle CGH are $60\°-60\°-60\°$

Triangle GHE

$m< EGH=90\°-2x=90-2(30\°)=30\°$

$m< GHE=4x=4(30\°)=120\°$

remember that

$m$

substitute and solve for m<GEH

$30\°+120\°+m$

$150\°+m$

$m$

The measures of triangle GHE are $30\°-120\°-30\°$

Evgesh-ka [11]2 years ago

3 0

Answer:

x=30 degress

Step-by-step explanation:

BIG BRAIN

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There are 75 people in a room. Of these people, 2/5 are from Germany. If 4/9 of the people who are not from Germany are from Fra

Alex Ar [27]

Answer:

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Step-by-step explanation:

1. You first want find out what is the number of people from Germany.

So you would find...

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2. Next you want to to find out the number of people from France.

So you would do the following...

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2 years ago

Read 2 more answers

Three trigonometric functions for a given angle are shown below. cosecant theta = thirteen-twelfths; secant theta = Negative thi

Kay [80]

Answer:

(–5, 12) is the correct answer.

Step-by-step explanation:

We are given the following values:

$cosec\theta = \dfrac{13}{12}\\sec\theta=-\dfrac{13}{5}\\cot\theta =-\dfrac{5}{12}$

Now, we know the following identities:

$sin \theta = \dfrac{1}{cosec\theta}\\cos \theta = \dfrac{1}{sec\theta}\\tan \theta = \dfrac{1}{cot\theta}$

Now, the values are:

$sin\theta = \dfrac{12}{13}\\cos\theta=-\dfrac{5}{13}\\tan\theta =-\dfrac{12}{5}$

Sine value is positive and cos, tan values are negative.

It can be clearly observed that $\theta$ is in 2nd quadrant.

2nd quadrant means, the value of $x$ will be negative and $y$ will be positive.

Let us have a look at the value of $tan\theta$ :

$tan\theta = \dfrac{Perpendicular}{Base}\\OR\\tan\theta = \dfrac{y-coordinate}{x-coordinate} = -\dfrac{12}{5}\\\therefore y = 12,\\x = -5$

Please refer to the attached image for clear understanding and detailed explanation.

Hence, the correct answer is coordinate (x,y) is (–5, 12)

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