Question

Two angles of a quadrilateral are 72degree and 56degree respectively and the remaining two angles are in the ratio of 3:5 find the measure of each angle of the quadrilateral

(With steps)

Answer 1

Step-by-step explanation:

Given :-

Two angles of a quadrilateral are 72° and 56° respectively and the remaining two angles are in the ratio of 3:5 .

To find :-

Find the measure of each angle of the quadrilateral ?

Solution :-

The two angles of a quadrilateral = 72° and 56°

The ratio of the other two angles = 3:5

Let they be 3X° and 5X°

We know that

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

=> 72° + 56° + 3X° + 5X° = 360°

=> 128° + 8X° = 360°

=> 8X° = 360° - 128°

=> 8X° = 232°

=> X° = 232°/8

=> X° = 29°

The value of X° = 29°

The value of 3X° = 3×29° = 87°

The value of 5X° = 5×29° = 145°

Answer:-

The measure of all angles in the given quadrilateral are 72°, 56°, 87° and 145°

Used formulae:-

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