Question

supplementary angle of 6
Show that each angle of rectangle is right angle.
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Answer 1

Answer:

Let, ABCD be a rectangle.

We have to prove that ∠A=∠B=∠C=∠D=90⁰

We know that a rectangle is parallelogram where its one angle is 90⁰

Let us assume ∠A=90⁰

Now,

AD∥BC [opposite sides of a parallelogram are parallel]

And AB is transversal.

So, ∠A+∠B=180

0

[interior angle are supplementary]

⇒90 ⁰

+∠B=180 ⁰

⇒∠B=90 ⁰

Again, we know that opposite angles of a parallelogram are equal.

∴∠C=∠A and ∠D=∠B

∴∠C=90 ⁰

and ∠D=90 ⁰

∴∠A=∠B=∠C=∠D=90 ⁰

Hence, it is proved that ABCD is a rectangle.