Question

two angle of a quadrilateral are in the ratio 2:4. If the average of there is 60 and other two angles are equal. find all angles of triangle​

Answer 1

Step-by-step explanation:

Given :-

Two angles of a quadrilateral are in the ratio = 2:4

The average of the angles is 60.

Other two angles are equal.

To find :-

All angles in the quadrilateral

Solution :-

Given that

The ratio of the two angles of a quadrilateral = 2:4

Let they be 2x° and 4x°

We know that

Average of two numbers a and b is (a+b)/2

Average of the given two angles

= (2x°+4x°)/2

= 6x°/2

= 3x°

According to the given problem

The average of the two angles = 60

=> 3x° = 60

=> x° = 60/3

=> x° = 20

The value of x = 20°

If x = 20° then 2x° = 2(20°) = 40°

If x = 20° then 4x° = 4(20°) = 80°

The two angles are 40° and 80°

And , Given that

The other two angles are equal

Let they be y° and y°

We know that

The sum of all the four interior angles in a quadrilateral is 360°

=> 40°+80°+y°+y° = 360°

=> 120° + 2y° = 360°

=> 2y° = 360°-120°

=> 2y° = 240°

=> y° = 240°/2

=> y° = 120°

Therefore, The other two angles are 120° and 120°

Answer :-

The four angles in the given quadrilateral are 40° , 80° , 120° and 120°

Check :-

The first two angles are 40° and 80°

Their ratio = 40: 80 = 2:4

Their average = (40°+80°)/2 = 12°0/2 = 60°

The other two angles are 120° and 120°

They are equal.

Verified the given relations in the given problem.

Used formulae:-

→ Average of two numbers a and b is (a+b)/2

→The sum of all the four interior angles in a quadrilateral is 360°

Answer 2

Refer the given attachment