Q. 14.7( 16 Votes )

# The adjacent angl

Answer :

Let us assume a parallelogram ABCD,

We know that the sum of the adjacent angles in a parallelogram is **180 ^{0}**.

We also know that the angles at the opposite vertices are equal.

i.e., **∠****A +** **∠****B = 180 ^{0}**. ...... - (1)

**∠****A =** **∠****C** ...... ...... (2)

**∠****B =** **∠****D** ...... ...... (3)

According to the problem, it is given that the adjacent angles are in the ratio of **2:1**.

Let us assume that the adjacent angles be A and B.

Let’s take the values of **∠****B = 2x** and **∠****A = x**

From eq(1) we get,

⇒ x + 2x = 180^{0}

⇒ 3x = 180^{0}

⇒

⇒ x = 60^{0}.

Now find the value of ∠A and ∠B,

⇒ ∠A = x

⇒ **∠****A = 60 ^{0}**

⇒ ∠B = 2x

⇒ ∠B = 2 × 60^{0}

⇒ **∠****B = 120 ^{0}**

From (2) and (3) we get,

**∠****C = 60 ^{0}** and

**∠**

**D = 120**

^{0}The values of **∠****A,** **∠****B,** **∠****C** and **∠****D** is **60 ^{0}, 120^{0}, 60^{0}, 120^{0}**.

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