Question

Two adjacent angles of a parallelogram are in the ratio 4 is to 5 find the measure of all its angles

Answer 1

80°,100°,80°,100°

Step-by-step explanation:

Let '4x' and '5x' be the adjacent angle of the parallelogram.

We know,

the sum of all interior angle of a parallelogram is 360°.

Therefore,

2(4x)+2(5x) = 360°.

or 8x+10x = 360°

or 18x = 360°

or x=360/18 (transferring 18 from LHS to RHS)

or x=20.

Since,

4*20= 80°

And

5*20= 100°

Therefore, the requrired measure of all the angles are 80°,100°,80°,100° (the opposite angles of a parallelogram are equal. Therefore, all the equal angles will be in opposite direction).