Question
In the given figure, show that: $\angle a =\angle b +\angle c$

(i) If $\angle b =60^{\circ}$ and $\angle c =50^{\circ}$; find $\angle a$.
(ii) If $\angle a =100^{\circ}$ and $\angle b =55^{\circ}$ : find $\angle c$.
(iii) If $\angle a =108^{\circ}$ and $\angle c =48^{\circ}$; find $\angle b$.

Answer

∵ AB || CD
∴ b = c and ∠A = ∠C ........(Alternate angles)
Now in Δ PCD,
Ext. ∠APC = ∠C + ∠D
⇒ a = b + c
(i) If b = 60°, c = 50°, then
a = b + c = 60° + 50° = 110°
(ii) If a = 100° and b = 55°,
then a = b + c
⇒ 100° = 55°+ c
⇒ c = 100°− 55° = 45°
(iii) If a = 108° and c = 48°
then a = b + c
⇒ 108° = b + 48°
⇒ b = 108°− 48° = 60°

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