Question 4. In Fig. 6.16, if x + y = w + z, then prove that AOB is a line. Chapter 6: Lines and Angles Maths Class 9 solutions are developed for assisting understudies with working on their score and increase knowledge of the subjects. Question 4. In Fig. 6.16, if x + y = w + z, then prove that AOB is a line. is solved by our expert teachers. You can get ncert solutions and notes for class 9 chapter 6 absolutely free. NCERT Solutions for class 9 Maths Chapter 6: Lines and Angles is very essencial for getting good marks in CBSE Board examinations
Question 4. In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.
Solution: Sum of all angles in a circle always 360°
Hence
∠AOC + ∠BOC + ∠DOB + ∠AOD = 360°
=> x + y + w + z = 360°
=> x + y + x + y = 360°
Given that x + y = w + z
Plug the value we get
=> 2w + 2z = 360°
=> 2(w + z) = 360°
w + z = 180° (linear pair)
or ∠BOD + ∠AOD = 180°
If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line
Hence AOB is a line.
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