Question

help with full solution

Answer 1

In ∆PQR,

angle RQP + angle QPR + angle PRQ = 180° (angle sum property of ∆)

Hence,
angle 1 + angle 6 + angle 2 = 180°
=> angle 1 + angle 2 + angle 6 = 180°....(1)

Similarly, in ∆ PRS,

angle SRP + angle RPS + angle PSR = 180° (angle sum property)

Hence,
angle 3 + angle 5 + angle 4 = 180°
=> angle 3 + angle 4 + angle 5 = 180°....(2)

Now, sum of all angle of PQRS = sum of angles of PQR + sum of all angles of PRS.

Hence, adding (1) and (2)

angles 1 + 2 + 6 + angles 3 + 4 + 5 = 180 + 180
=> angles 1 + 2 + 3 + 4 + 5 + 6 = 360°

Hence, sum of all angles of PQRS is 360°.

$\red{Hope\: this \: helps}$

Answer 2

angles(1+2+6)=180degrees [Sum of angles of triangle is 180]

angles(3+4+5)=180degrees [Sum of angles of triangle is 180]

Sum of angles of any quadrilateral is 36o degree

Hope you get your answer