Question

Exercis
The sum of two angles of a quadrilateral is 160
The other two angles are in the ratio 2 : 3. Find
the angles.​

Answer 1

The sum of two angles of an quadrilateral is 160°.

Let $\angle{1}\:+\:\angle{2}$ = 160°

The other two sides are in the ratio 2:3.

Let third angle be 2M and fourth angle be 3M.

Now,

Sum of all angles of quadrilateral is 360°.

So,

$\angle{1}\:+\:\angle{2}\:+\:\angle{3}\:+\:\angle{4}$ = 360°

=> 160° + 2M + 3M = 360°

=> 5M = 360° - 160°

=> 5M = 200°

=> M = 40°

So,

Third angle :-

=> 2M

=> 2(40°)

=> 80°

Fourth angle :-

=> 3M

=> 3(40°)

=> 120°

∴ The angles are 80° and 120°.

_______________________________

☆ VERIFICATION :

=> $\angle{1}\:+\:\angle{2}\:+\:\angle{3}\:+\:\angle{4}$ = 360°

=> 160° + 80° + 120° = 360°

=> 360° = 360°