If the four interior angles of a quadrilateral are (p + 10)o, (p – 30)o, (2p – 450o, and (p + 15)o, then p is

A.
125^{o} 
B.
82^{o} 
C.
135^{o} 
D.
105^{o} 
E.
60^{o}
Correct Answer: Option B
Explanation
Sum of interior angles of a polygon = (2n – 4) x 90
where n is the no. of sides
sum of interior angles of the quad. = ({2 x 4} 4) x 90
(8 – 4) x 90 = 4 x 90o
= 360o
(p + 10)o + (p – 30)o + (2p – 45)o + (p + 15)o = 360o
p + 10o + p – 30o + 2p – 45o + p + 15 = 360o
5p = 360o + 50o
= 82o