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In the figure below, what is the sum of p and q?
  • a)
    75°
  • b)
    150°
  • c)
    180°
  • d)
    285°
  • e)
    360°
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In the figure below, what is the sum of p and q?a)75°b)150°c)1...
To solve this problem, set up three other variables, x, y, and z. Let x be the supplement of angle p. Let y be the supplement of angle q. Let z be the angle opposite of the 105° angle, so z = 105°. With these new variables, you know that p = 180 - x and q = 180 - y. This means that p + q = (180 - x) + (180 - y), which simplifies to 360 - (x+y). You can see that the three lines form a triangle and that one of the angles is 105°. That means that the other two angles, x and y must have a sum of 180 - 105, or 75°. Thus, if x + y = 75°, then p + q = 360 - (x + y), or 360 - 75, which is 285°.
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