Question

find the value of x and solve fast

Answer 1

Hey

Here is your answer,

let RPS be y.

QPR + RPS = 90 (RIGHT ANGLES TRIANGLE)
50+y=90
Y=90-50
Y=40°

Angle sum property of a triangle PRS =180°
Y+30°+PRS=180°
PRS=180-(30+40)
PRS=180-70
PRS=110°

PRQ = 180-110
=70

Angle sum property of a triangle PRQ= 180°
X+30+70=180
X=180-(70+30)
X=180-100
X=80°

Hope it helps you!

Answer 2

angle pqs+qsp+spq=180* (sum of a Δ)
in Δprs,
   pr=rs
therefore,
   angle rps=angle prs
angle rps= 30*
therefore  angle qpr+angle rps=70*+30*=100*

therefore, angle p+q+s=180*
100*+q+30*=180*
q+130*=180*
q=180*-130*
q=50*

hope it will help you.