Question

Complete the paragraph proof.

Answer 1

(a) ∠1 + ∠2 = 180° , (b) ∠2 + ∠3 = 180°

(c) ∠1 + ∠2 = ∠2 + ∠3 (EUCLID's LEMMA)

(d) ∠1 = ∠3 , (e) ∠1 ≅ ∠3

Explanation:

SUPPLEMENTARY ANGLES: Two angles are said to be supplementary angles if they add up to a measure of 180°.

Now, here ∠1 , ∠2 and ∠2 ,∠3 are supplementary angles.

⇒ (a) ∠1 + ∠2 = 180°.

and (b) ∠2 + ∠3 = 180°

Now, as both the sum are equivalent to 180°.

Hence, (c) ∠1 + ∠2 = ∠2 + ∠3 (EUCLID's LEMMA)

Now, subtraction ∠2 from both sides, we get

(d) ∠1 = ∠3

or, (e) ∠1 ≅ ∠3