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Lines and Angles — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSLines and Angles4 Marks
Question
The game of billiards is played with balls placed on a rectangular table. One ball is struck with the
end of a stick, called a cue. The ball bounces into other balls and relects off the sides of the table. In a real game, the ball may spin, but for mathematical purposes, it is considered that the ball travels in a straight line with the same relection and incidence angles.

Image

On a billiard table ABCD, the ball placed at O is struck with the cue.
1. What is the value of ∠a + ∠d?
2. Why is the line OM parallel to PN?

✓

Answer

1. 90
   90°
2. Mathematically valid proof
● Let angles on line AMB be a, x and b and angles on line BNC be c, y and d.
x = 180 – (a + b) …..1
y = 180 – (c + d) …...2
 Adding 1 and 2,
x + y = 360 – (a + b + c + d)
  = 360 – (2a + 2c)
  = 360 – 2 × 90 = 180
Thus, lines OM and NP are parallel. 

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