Question

Angle aed congruent angle abc, ad = 3 , db = 5 ae = 4 then the length of ac isa)2b)6c)8d)12​

Answer 1

Option ( b ) 6 .

Length of ∠AC = 6.

Given

To find the length of ∠AC.

∠AED is congruent to ∠ABC ( ∠AED ≅ ∠ABC ).

Where, ∠A is common.

Therfore,  ∠AED ≅ ∠ABC .

∠AED and ∠ABC is proportional to each other.

                 ∠AE / ∠AB = ∠AD / ∠AC

Where, ∠AB = ∠AD + ∠DB ( refer the figure for better understanding )

Now, apply the values, ∠AD = 3  ;  ∠DB = 5 ;  ∠AE = 4

                 ∠AE / ∠AB = ∠AD / ∠AC

                 ∠AE / ∠AD + ∠DB = ∠AD / ∠AC

                  4 / ( 3 + 5 ) = 3 / ∠AC

                            4 / 8 = 3 / ∠AC

                             1 / 2 = 3 / ∠AC

                               ∠AC = 6.

Therefore, the length of ∠AC = 6.

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