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If the four interior angles of a quadrilateral are (p + 10)°, (p - 30)°,...

Mathematics
JAMB 1978

If the four interior angles of a quadrilateral are (p + 10)°, (p - 30)°, (2p - 45)°, and (p + 15)°, then p is

  • A. 125o
  • B. 82o
  • C. 135o
  • D. 105o
  • E. 60o
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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


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