Question

the exterior angle PRS of triangle PQR is 105degrees. if q= 70degrees, find angleP. is anglePRS greater than angleP

Answer 1

in triangle PQR,
angle Q = 70 degree
angle PRS = 105 dergrees
let angle QRP be angle 1, then;
angle 1+ 105 degree = 180 degree (linear pair)
angle 1 = (180 - 105) degrees
             = 75 degree
now, since we have angle Q = 70 degree, and
                                 angle 1 = 75 degree 
let the unknown angle i.e. angle P be x degrees
now, angle (Q + 1 + x) = 180 degrees (angle sum proplerty of a triangle)
      (70 + 75 + x) degrees  = 180
       (145 + x )degrees = 180 
     x = (180 - 145)
        = 35 degrees
therefore angle P = 35°

Answer 2

∠PRS=105°
∠PQR=70°
we know that ,
exterior angle of a triangle is equal to sum 2 opposite angles in a triangle
⇒∠PRS=∠PQR+∠QPR
⇒105°=70°+∠QPR
⇒∠QPR=35°