Question

solve this problem please help me

Answer 1

ʜᴇʟʟᴏ ᴍᴀᴛᴇ!

As given in figure; AB || CD

Therefore, /_ ACE = /_ BAC = 75° [ Alternate Angles ]

Now, /_ ACE + /_ ECF = 180° [ Linear Pair ]
75° + /_ ECF = 180°
/_ ECF = 105°

Now,

/_ ECF + /_ CFE + /_ FEC = 180° [ Angle Sum property of ∆ ]

105° + 30° + x = 180°
x = 180° - 135° = 45°

Hence your answer is 45°

$\boxed{Hope\:it\:helps\:you!}$

Answer 2

Given AB || CD

So, sum of angle CAB and angle DCA = 180°


75° +angle DCA = 180°

angle DCA = 105°





We Know opposite angles are equal, so

angle DCA = angle ECF

=> 105° = angle ECF




In ∆ FEC,

sum of angles at vertices = 180°

Angle ECF + angle CFE + x = 180

105° + 30° + x = 180°

x = 180 - 135

x = 45°






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