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Tanzania [10]
3 years ago
10

Given m||n, find the value of x. + (2x-26) (7x+8)​

Mathematics
2 answers:
melomori [17]3 years ago
6 0

Answer:

value of x is 22°

Step-by-step explanation:

Correct answer

horsena [70]3 years ago
5 0

Given :

m||n, interior angles are (2x-26) and (7x+8).

To Find :

Find the value of x.

Solution :

We know, alternate interior angle of a triangle are supplement to each other.

So, (2x-26) + (7x+8) = 180°

9x - 18° = 180°

9x = 198°

x = 22°

Therefore, the value of x is 22°.

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If the average of nine consecutive integers is zero, what is the largest integer?
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Answer:

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-4, -3, -2, -1, 0, 1, 2, 3, 4

So the largest integer is 4.

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In ∆MNP, m∠N = 90º, NH – altitude, m∠P = 21º, PM = 4 cm. Find MH.
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Answer:

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Step-by-step explanation:

In right triangle MNP, MP = 4 cm, m∠N = 90°, m∠P = 21°

By the sine definition,

\sin \angle P=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{MN}{MP}\\ \\MN=MP\sin \angle P\\ \\MN=4\sin 21^{\circ}\approx 1.43\ cm

Now, consider right triangle HMN (it is right because NH is an altitude). By the cosine definition,

\cos \angle M=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{MH}{MN}\\ \\MH=MN\cos \angle M

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m\angle M=90^{\circ}-m\angle P=90^{\circ}-21^{\circ}=69^{\circ}

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MH=1.43\cos 69^{\circ}\approx 0.51\ cm

7 0
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