Question

M<p= 21x+25 and m <n= 675x-27/3

Answer 1

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

$m\angle p=21x+25\\\\m\angle n=\dfrac{675x-27}{3}=\dfrac{675x}{3}-\dfrac{27}{3}=225x-9$

therefore

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

$m\angle p=21x+25$

substitute

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

$m\angle n=225x-9$

substitute

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