On figure arrow head segement are parellel then find the value of x and y

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On figure arrow head segement are parellel then find the value of x and y

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Valentina 1 month 2021-10-28T01:05:29+00:00 1 Answer 0 views 0

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    2021-10-28T01:07:27+00:00

    Answer:

    Answer:

    x=40° and y=40°

    Step-by-step explanation:

    ∠FCG=∠BCE=105°( vertically opposite angles)

    Now, using the straight angle property, ∠BCA+∠BCE+∠ECD=180°

    ⇒35°+105°+y=180°

    ⇒y=40°

    Also, ∠BCD=∠BCE+∠ECD

                       = 105°+40°

           ∠BCD  = 145°

    Now, ∠BCA+∠ACF+∠FCG=180°

    ⇒35°+∠ACF+105°=180°

    ⇒∠ACF=40°

    Therefore, ∠BCF=75°

    Now, ∠1=∠BCF=75°(Alternate angles)

    Also, ∠1+∠ABC=180°(Straight angle property)

    ∠ABC=180-75

    ∠ABC=105°

    Now, using Angle sum property in triangle ABC,

    ∠BAC+∠ABC+∠BCA=180°

    x+105°+35°=180°

    x=40°

    Thanks…

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