Question

in triangle abc ad divides ∠bac in the ratio 2 : 3 and bd = ad. if side ba is produced to e such that ∠case = 1150 then ∠acb =

Answer 1

In triangle abc ad divides ∠bac in the ratio 2 : 3 and bd = ad. if side ba is produced to e such that ∠case = 1150 then ∠acb =

Correction: In the given question, ∠case = 1150 should be ∠cae = 115°

Solution: From the attached diagram,

In Δabc, ad divides ∠bac in the ratio 2 : 3 and bd = ad.

Let the common ratio be 'x', then ∠bad = 2x and ∠cad = 3x

∠bad + ∠cad + ∠cae = 180° -- - --------using straight line angle property.

or, 2x + 3x + 115° = 180°

or, x = 13°

Again side bd = ad

So, by using the property of triangle, equal sides corresponds equal angles

∠abd = ∠bad = 2x = 2× 13° = 26°

and ∠dac = 3x = 39°

Again, we shall apply the sum angle property of the triangle in Δabc,

∠abc + ∠bac + ∠acb = 180°

or, 26° + 65° + ∠acb = 180°

or, ∠abc = 89°