Answer :

Consider a Parallelogram **ABCD**,

It is told that the side **BC** is produced to **E** and **∠****BCE = 105 ^{0}**.

From the figure, we can say that

**∠****BCE +** **∠****BCD = 180 ^{0}** (Since ∠DCE is the straight angle)

By substituting the values we get,

⇒ 105^{0} + ∠BCD = 180^{0}

⇒ ∠BCD = 180^{0} - 105^{0}

⇒ **∠****BCD = 75 ^{0}**

We know in a parallelogram the opposite angles are equal and the sum of the adjacent angles is 180^{0}.

i.e, **∠****C =** **∠****A** ...... (1)

**∠****B =** **∠****D** ...... (2)

**∠****C +** **∠****D = 180 ^{0}** ...... (3)

From Eq(1) we can write

**∠****A = 75 ^{0}**.

From Eq(3), we can write

⇒ 75^{0} + ∠D = 180^{0}

⇒ ∠D = 180^{0} - 75^{0}

⇒ **∠****D = 105 ^{0}**.

From Eq(2), we can write

**∠****B = 105 ^{0}**.

The angles **∠****A,** **∠****B,** **∠****C,** **∠****D** are**75 ^{0}, 105^{0}, 75^{0}, 105^{0}**.

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