If the four interior angles of a quadrilateral are (p + 10)^\circ, (p - 30)^\circ, (2p - 45)^\circ, and (p + 15)^\circ, then p is
A
125o
B
82o
C
135o
D
105o
E
60o
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #32699)