Respuesta :

gmany

∠n and ∠p are supllementary angles, therefore m∠n + m∠p = 180°.

[tex]m\angle p=21x+25\\\\m\angle n=\dfrac{675x-27}{3}=\dfrac{675x}{3}-\dfrac{27}{3}=225x-9[/tex]

therefore

[tex](21x+25)+(225x-9)=180\\\\(21x+225x)+(25-9)=180\\\\246x+16=180\qquad|-16\\\\246x=164\qquad|:246\\\\x=\dfrac{164}{246}\\\\x=\dfrac{2}{3}[/tex]

[tex]m\angle p=21x+25[/tex]

substitute

[tex]m\angle p=21\cdot\dfrac{2}{3}+25=7\cdot2+25=14+25=39^o[/tex]

[tex]m\angle n=225x-9[/tex]

substitute

[tex]m\angle n=225\cdot\dfrac{2}{3}-9=75\cdot2-9=150-9=141^o[/tex]

MrRoyal

Angles on a straight line add up to [tex]180^o[/tex].

  • The value of x is [tex]\frac 23[/tex].
  • The measure of [tex]\angle p[/tex] is [tex]39^o[/tex].
  • The measure of [tex]\angle n[/tex] is [tex]141^o[/tex]

Given that:

[tex]\angle p = 21x + 25[/tex]

[tex]\angle n = \frac{675x - 27}3[/tex]

To calculate the value of x, we use:

[tex]\angle p + \angle n = 180^o[/tex] --- angle on a straight line.

So, we have:

[tex]21x + 25 + \frac{675x - 27}{3} = 180[/tex]

[tex]21x + 25 + 225x - 9 = 180[/tex]

Collect like terms

[tex]21x + 225x = 180 + 9 - 25[/tex]

[tex]246x = 164[/tex]

Divide both sides by 246

[tex]x = \frac 23[/tex]

To calculate the measures of p and n, we substitute [tex]x = \frac 23[/tex] in

[tex]\angle p = 21x + 25[/tex]

[tex]\angle n = \frac{675x - 27}3[/tex]

So, we have:

[tex]\angle p = 21x + 25[/tex]

[tex]\angle p = 21 \times \frac 23 + 25[/tex]

[tex]\angle p = 39[/tex]

[tex]\angle n = \frac{675x - 27}3[/tex]

[tex]\angle n = \frac{675 \times 2/3 - 27}{3}[/tex]

[tex]\angle n = 141[/tex]

Hence, the value of x is 2/3.

Read more about angles on straight lines at:

https://brainly.com/question/17104958