Question

three angles of a quadrilateral are in the ratio 1:2:3. the sum of the least and the greatest of these angles is equal to 180°. find all the angles of this quadrilateral
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Answer 1

Given:

The angle of quadrilateral is in ratio 1:2:3

the sum of the least and the greatest of these angles is equal to 180°

To find:

All the angles of the quadrilateral

Solution:

Let x to be included in the ratio , then the ratio becomes x , 2x , 3x

According to question ,

Sum of the smallest angle and the greatest angle of the quadrilateral is 180°.

x + 3x = 180°

4x = 180°

x =( 180/4)°

x = 45 °

Now , these 3 angles of quadrilateral are :

x = 45°

2x = 2×45° =90°

3x = 3×45° = 135°

We know that ,

Sum of all angles of the quadrilateral is 460°

45° + 90° + 135° + x = 360°

270° + x = 360°

x = 360° - 270°

x = 90°

$\bold{all \: the \: angles \: of \: quadrilateral \: are} \\ \boxed {\bold{ \sf \red{45 \degree \: 90 \degree \: 135 \degree \: and \: 90 \degree}}}$

Answer 2

Answer:

★ 30° , 60° , 90° and 180° ★

Step-by-step explanation:

Given:

• Three angles of quadrilateral are in ratio 1:2:3
• Sum of least and greatest of these angles is equal to 180°

To Find:

• Measure of all the angles of the quadrilateral.

Solution: Let x be the common in given ratio.

• 1x : 2x : 3x = 180°

$\small\implies{\sf }$ x + 2x + 3x = 180

$\small\implies{\sf }$ 6x = 180

$\small\implies{\sf }$ x = 180/6

$\small\implies{\sf }$ x = 30°

Hence, Measure the measure of these angles are:-

→ x = 30°

→ 2x = 2(30) = 60°

→ 3x = 3(30) = 90°

• We know that the sum of all angles of a quadrilateral is 360°

• Let the forth angle of quadrilateral be ∠4.

$\small\implies{\sf }$ 30 + 60 + 90 + ∠4 = 360°

$\small\implies{\sf }$ 180° + ∠4 = 360°

$\small\implies{\sf }$ ∠4 = 360° – 180°

$\small\implies{\sf }$ ∠4 = 180°

Hence, The measure of all angles of quadrilateral are : 30° , 60° , 90° and 180°