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Answer:

[tex]x[/tex] = 3°

[tex]z[/tex] = 106°

Step-by-step explanation:

Since the angles are opposite each other, we know that [tex]9x+47[/tex] = 74°. We can use this information to solve for [tex]x[/tex]:

74° = [tex]9x+47[/tex]

27° = [tex]9x[/tex]

3° = [tex]x[/tex]

Since we know the whole system has to add up to 360°, or one rotation we can find what [tex]z[/tex] + the angle opposite it is equal to, and from there find [tex]z[/tex]:

360° = 2(74°) + 2[tex]z[/tex]

360° = 148° + 2[tex]z[/tex]

212° = 2[tex]z[/tex]

106° = [tex]z[/tex]

TheAmethyst

Question : -

Given the figure below , find the values of x and z

Given : -

  • Angle 1 = 74°

  • Angle 2 = z°

  • Angle 3 = ( 9x + 47 ) °

To find : -

  • Values of x and z

Concept : -

For doing such types of questions we must have concept and knowledge of linear pairs of angles and vertically opposite angles .

So let's Starting the Solution : -

As we know that Angle 1 and Angle 3 are vertically opposite angles . Therefore , we can equate them and easily find the value of x . So :

  • 9x + 47 = 74

  • 9x = 74 - 47

  • 9x = 27

  • x = 27/9

  • x = 3°

Therefore , value of x is 3° .

Now Verifying :

  • 9 ( x ) + 47 = 74

  • 9 ( 3 ) + 47 = 74

  • 27 + 47 = 74

  • 74 = 74

  • L.H.S = R.H.S

  • Hence , Verified .

Therefore , our value for x is correct .

Now , finding value of z :

As we know that Angle 1 and Angle 2 are Linear pair . Therefore , there sum is equal to 180° . So :

  • z + 74° = 180°

  • z = 180° - 74°

  • z = 106°

Therefore , value of z is 106° .

Now Verifying :

  • 106° + 74° = 180°

  • 180° = 180°

  • L.H.S = R.H.S

  • Hence , Verified .

Therefore, our answer is correct .

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