Question

The angles of the quadrilateral are in the ratio 2:5:4:1. Which of the following is true? 


Largest angle in the quadrilateral is 150°

Smallest angle is 40°

The second largest angle in the quadrilateral is 80°

None of these

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Answer 1

Given-

• Ratio of the angles of quadrilateral
• 2:5:4:1

To Find

• all angles

Concept used

• Sum of all angles of quadrilateral=360

Solution

Let the common ratio be x

• Angle 1st=2×x=2x
• Angle 2nd=5×x=5x
• Angle 3rd=4×x=4x
• Angle 4th =1×x=x

We know sum of all angles of quadrilateral is 360

$\therefore \bf 2x + 5x + 4x + x = 360 \\ \implies \bf 12x = 360 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \bf \: x = \frac{360}{12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \boxed{ \bf \ \: x = 30} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\bf \: angle1 = 2 \times 30 = 60 \\ \bf \: angle2 = 5 \times 30 = 150 \\ \bf \: angle3 = 4 \times 30 = 120 \\ \bf \:angle4 = 1 \times 30 = 30$

Answer 2

Given:

The ratio of angles of quadrilateral = 2:5:4:1

To find:

The angle of quadrilateral that matches with the correct statement given=?

Solution:

The steps for finding the angle of quadrilateral are given below:

Step I: Assume the values

=> Let the first angle be = 2x

=> Let the second angle be= 5x

=> Let the third angle be = 4x

=> Let the fourth angle be = 1x (from the ratio given)

=> We know that sum or addition of all the angles which are interior in the quadrilateral gives total answer as 360°.

Step II: Find value of "x"

∴ 2x + 5x + 4x + 1x = 360°

=> 12x = 360°

=> x = $\frac{360}{12}$

=> x = 30

Step III: Find the measure of all the interior angles of quadrilateral

=> 2x = 2× 30 = 60°

=> 5x = 5× 30 = 150°

=> 4x = 4× 30 = 120°

=> 1x = 1× 30 = 30°

From the above measure of angles, we get the correct statement which is: Largest angle in the quadrilateral is 150° (1st option).