Question

In triangle ABC, AC = BC and AD = DC = CE = BE. FD ║ CE. If ∠CAB = 35°, then what is the value of 'x'?

Answer 1

x° = 40°

Step-by-step explanation:

In∆ABC angle CAB = angle CBA. as AC = BC {Angles opposite to equal sides are always equal}

so, angle CBA = 35°

now, In ∆ADC angle CAD = angle ACD as AD = CD {angles oposite to equal sides are equal }

so, angle ACD= 35°

similarly,In ∆BEC angle BCE is 35° as CE = BE{angle opposite to equal sides are always equal}

let angle ECD be y

now, In ∆ABC. angle CAB +angle CBA +angle ACB = 180° { by angle sum property}

so, 35°+35°+angle ACD+angle ECD + angle BCE

i.e. 35° + 35+° 70+y°=180°

70°+70°+y = 180°

140°+y = 180°

y = 180°-140°

y = 40°

as,FD||CE so, angle FDC = angle ECD{ Alternate Interior angles are equal}.

therefore angle FDC which is x will be 40°