Can someone check my answers to see if they're correct?

Mathematics

1 answer:

Sati [7]3 years ago

3 0

Answer:

a = 125°

b = 55°

c = 55°

d = 55°

e = 125°

f = 55°

Step-by-step explanation:

See the attached diagram.

The angles (x + 75)° and (2x + 25)° are the alternate angles and they are equal.

So, x + 75 = 2x + 25

⇒ x = 50

Hence, (x + 75)° = (50 + 75)° = 125°.

Now, from the given diagram it is clear that

a = (x + 75)° = (2x + 25)° = e = 125°

And, b = c = d = f = 55°

This is because, a and b are supplementary angles and their sum will be 180°.

So, a + b = 180°

⇒ 125° + b = 180°

⇒ b = 55°

So, b = c = d = f = 55° (Answer)

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X is in the second quadrant means that x/2 is in the first quadrant.

Consider the right triangle drawn in the figure. Let tan(x/2)=a.

Then, let the length of the opposite side to x/2 be a, the adjacent side be 1 and the hypotenuse be square root of a squared +1, as shown in the figure.

sin(x/2)=|opp side|/ |hypotenuse| = $\frac{a}{ \sqrt{ a^{2}+1 } }$

cos (x/2) = |adj side|/ |hypotenuse| = $\frac{1}{ \sqrt{ a^{2}+1 } }$

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