In Fig. 9.30, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ ACD = 105° and ∠ EAF = 45°, find all the angles of the Δ ABC .

Question

In Fig. 9.30, the sides BC, CA and AB of a &#x394; ABC have been produced to D, E and F respectively. If &#x2220; ACD = 105&#xB0; and &#x2220; EAF = 45&#xB0;, find all the angles of the &#x394; ABC .

Philoid · Accepted Answer

Given,

∠ACD = 105^o

∠EAF = 45^o

∠EAF = ∠BAC (Vertically opposite angle)

∠BAC = 45^o

∠ACD + ∠ACB = 180^o (Linear pair)

105^o + ∠ACB = 180^o

∠ACB = 180^o – 105^o

= 75^o

In

∠BAC + ∠ABC + ∠ACB = 180^o

45^o + ∠ABC + 75^o = 180^o

∠ABC = 180^o – 120^o

= 60^o

Thus, all three angles of a triangle are 45^o, 60^o and 75^o.

In Fig. 9.30, the sides BC, CA and AB of a Δ ABC have been produced to D, E and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the Δ ABC.