Question

5. Find the
Find the value of a and b in each of the
following cases:
​

Answer 1

Answer: i) a = 48°

              ii) a = 35°  b = 80°

              iii) a = 58°  b = 55°

Step-by-step explanation:

i) AB ll CD

EG acts as a transversal

so ∠a = ∠EGF = 48° ( alternate interior ∠s )

ii) QS = QR  ⇒ ΔQRS is an isosceles Δ

∴ base angles must be equal.

⇒ ∠QSR = ∠b = 80°

∠P + ∠b + ∠PQR = 180° ( angle sum property )

⇒ 45° + 80° + ∠a + ∠SQR = 180°  ---( i )

and ∠QSR + ∠b + ∠SQR = 180° ( angle sum property )

       ⇒ 80° + 80° + ∠SQR = 180°

       ⇒ ∠SQR = 20°

In ( i )

⇒ 45° + 80° + ∠a + ∠SQR = 180°

⇒ 45° + 80° + ∠a + 20° = 180°

⇒ ∠a = 35°

iii) AB ll EC and AC acts as a transversal

⇒ ∠a = ∠ACD ( alternate interior angles )

in ΔADC, 62° + ∠ACD = 120° ( exterior angle property )

⇒ ∠ACD = 58°

∴ ∠a = 58°

In ΔABC, ∠a + 67° + ∠b = 180° ( angle sum property )

⇒ 58° + 67° + ∠b = 180°

⇒ ∠b = 55°

Hope this helps!! I coudnt get ∠b for the first one tho... sorry..