Answer:
(a) ∠1 + ∠2 = 180° , (b) ∠2 + ∠3 = 180°
(c) ∠1 + ∠2 = ∠2 + ∠3 (EUCLID's LEMMA)
(d) ∠1 = ∠3 , (e) ∠1 ≅ ∠3
Step-by-step 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
