Question

One angle of a quadrilateral is 108 degree and the remaining angles are in the ratio 1 : 2 : 3. Find the remaining angles

Answer 1

Let the ratio be x.

First angle = 108°

Second angle = x°

Third angle = 2x°

Fourth angle = 3x°

We know that "Sum of all interior angles of a quadrilateral is 360°."

So,

    108° + x° + 2x° + 3x° = 360°

=> 6x° = 192°

=> x° = 32°

Hence remaining angles are

Second angle = 32°

Third angle = 64°

Fourth angle = 96°

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Answer 2

Answer -

• The remaining angles of the quadrilateral are 42°, 84° and 126°.

To find -

• The remaining angles of the quadrilateral.

Step-by-step explanation -

• Here, it is given that one angle of a quadrilateral is 108° and the remaining angles are in the ratio 1 : 2 : 3. We hahe to find the remaining angles!

Let -

• The remaining angles be "x", "2x" and "3x".

We know that -

$\bigstar \: \underline{\boxed{\sf Sum \: of \: all \: angles_{(quadrilateral)} = 360^{\circ}}}$

Therefore -

$\bf \mapsto x + 2x + 3x + 108 = 360$

$\mapsto \bf 6x + 108 = 360$

$\bf\mapsto 6x = 360 - 108$

$\mapsto \bf 6x = 252$

$\mapsto \bf x = \cancel{\dfrac{252}{6}}$

$\bf \mapsto x = 42^{ \circ}$

• The value of x = 42°.

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Hence, the remaining angles of the quadrilateral are -

$\tt x = 42^{ \circ}$

$\tt2x = 2 \times 42 = {84}^{ \circ}$

$\tt3x = 3 \times 42 = 126^{ \circ}$

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