Question

10. If two straight lines intersect each other in such a way that one of the
angles formed measures 90°, show that each of the remaining angles
measures 90°​

Answer 1

Given, two straight lines intersect each other in such a way that one of the angles formed measure 90°.

We know that, lines which intersect to form a right angle are known as perpendicular lines

In the above figure , AB is perpendicular to CD

Considering ∠AOC=90°

Now,

∠AOC+∠AOD=180° [Linear pair]

90°+∠AOD=180°

∠AOD=90°

Similarly,

∠AOC+∠BOC=180° and ∠BOD+∠AOD=180° [Both making linear pair]

So, we get ∠BOC=90° and ∠BOD=90°

Hence, ∠AOC=∠AOD=∠BOC=∠BOD=90°

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Answer 2

here is ur answer madam ji and % real answer not copied and plz spcht pr on ajao abhi

From the diagrame we know that ∠AOC and ∠BOD are vertically opposite angles ∠AOC = ∠BOD = 90o From the figure we also know that ∠AOC and ∠AOD form a linear pair So it can be wrtn as ∠AOC + ∠AOD = 180o Sbsttng the values 90o + ∠AOD = 180o On the ∠AOD = 180o – 90o By subtraction ∠AOD = 90o From the figure we also know that ∠BOC = ∠AOD are vertically opposite angles ∠BOC = ∠AOD = 90o so, it is proved that each of the remaining angle is 90degree.