Mathematics

In figure, which one of the following is not true ?


ANSWER

$$\angle 2+\angle 3=180^o$$


SOLUTION
Given, $$PQ$$ parallel to $$RS$$ and line $$l$$ is a transversal.
$$\therefore \angle 2+\angle 5=180^0$$   (1).....[ Co-interior angles=supplementary angles ]
$$\angle 3+\angle 8=180^0$$    (2) ..... [ Co- interior angles=supplementary angles ]
$$\angle 1=\angle 2$$   (3)..... [ Vertically opposite angles ]
$$\therefore \angle 1+\angle 5=180^o$$ [ By equation (1) and (3)]
$$\angle 2=\angle 3$$ [ Alternate interior angles ]
However, $$\angle 2 +\angle 3=180^o$$ cannot be true.
Hence, option $$D$$ is correct.
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Single Correct Medium Published on 09th 09, 2020
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