Question

In a quadrilateral, three angles are in the ratio of 3:3:1 and the fourth angle is 80 degrees. Find the measure of equal angles.

Answer 1

Sum of angles in a quadrilateral will be 360degree.
Fourth angle is given which is 80degree.
Angle remaining=360-80= 280degree.
The remaining three angles are in ratio 3:3:1
We'll Divide 280 degree in 3:3:1 ratio
Let remaining angles be 3x,3x and x respectively.
3x+3x+x= 280 degree.
7x = 280degree.
Therefore x=280/7= 40 degree.
Hence the measure of equal angles be 3x
=3*40=120 degree
Angles will be 120,120,40,80) degree, the sum of which is 360 degree.
Hope this helps.

Answer 2

Given,  ratio  is  3:3:1  and  fourth  angle  is  80°.

Sum  of  all  the  angles  of  the  quadrilateral  is  360°.

Let  the  ratio  numbers  be:

3x,  3x  and  1x

3 + 3 + 1 = 7

3x  +  3x  +  1x  +  80°  =  360°

7x  +  80°  =  360°

7x  =  360°  -  80°

7x  =  280°

3x  =  3 / 7 x 280°

     =  3 x 40

     =  120°

3x  =  3 / 7 x 280°

     =  3 x 40

    =  120°

1x  =  1 / 7 x 280°

    = 1 x 40

   =  40°

Therefore,  the  four  angles  are  120°,  120°,  40°  and  80°.