Question

The angles of quadrilateral are in the ratio of 1:2:3 sum is 180 degree find another angle

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Answer 1

Given that : The angles of quadrilateral are in the ratio of 1:2:3 sum is 180 degree

Let, the angles be x , 2x , and 3x

According to the question :

x + 2x + 3x = 180

=> 6x = 180

=> x = 30

Then, angles are : 30°, 2×30 = 60° and 3×30 = 90°

And the another angle of quadrilateral = 360-180 = 180° ( Sum of angles of the quadrilateral = 360°)

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Answer 2

Correct Question : Three angles of a quadrilateral are in the ratio of 1:2:3. The sum of the smallest and greatest angle is 180°. Find all the angles of a quadrilateral.

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$\boxed{\boxed{\mathtt{ Answer = 90°}}}$

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Now, According to the question

All the three angles of quadrilateral are in the ratio of 1:2:3

so, the 1st angle = x

2nd angle = 2x

3rd angle = 3x

let another angle = P

We know, sum of all the angles of a quadiletral = 360°

$\implies$ so, x + 2x + 3x + P = 360°

$\implies$ 6x + P = 360°

$\implies$ Here, Smallest angle + Greatest angle = 180°

$\implies$ x + 3x = 180°

$\implies$ 4x = 180°

$\implies$ x = 180°/4 = 45°

so, P = 360° ― 6 × 45° = 90°

$\implies$ Hence, all the angles are ;

$\implies$ x = 1 × 45° = 45°

$\implies$ 2x = 2 × 45° = 90°

$\implies$ 3x = 3 × 45° = 135°

$\implies$ and, P = 90°