Question

The average of 3 angles of a quadrilateral which are in the ratio 2::5:4 is 77 degrees. Find all the angles of a quadrilateral.

Answer 1

Question :

The average of 3 angles of a quadrilateral which are in the ratio 2::5:4 is 77 degrees. Find all the angles of a quadrilateral.

Answer :

The required angles of the quadrilateral are = 42°,105°,84°,129° .

For full solution refer to the above attachment.

Answer 2

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★Let the common ratio of angles be x.

Hence ,

★The angles are 2x, 5x and 4x

Given :-

=>Average of the 3 angles of the quad. =77

=>2x + 5x + 4x/ 3 = 77

=>11x°/3= 77°

=>11x°. =77° × 3

=>11x = 231

=>x = 21°

Hence , The angles are as follows:-

2x = 2×21° =42°
4x= 4×21=84°
5x=5 ×21=105°

As we know that,

Sum of all angles of a quad =360°

42+ 84 + 105 + angle ABC = 360°

angle ABC =360°-231° =129 °

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Hope It helps Uh !