Question

The adjacent angle a Parallelogram are in the ratio 5:4 find the measure of each of the angle of a parallelogram​

Answer 1

SOLUTION

Given,

The adjacent angle of a ||gm in ratio=5:4

Let the ratio be x

=) 5x+4x= 180° (adjacent angle)

=) 9x= 180°

=) x= 180°/9

=)x= 20°

Now,

1st angle = 5x, 5× 20° = 100°

2nd angle= 4x, 4×20°= 80°

hope it helps ☺️

Answer 2

Given:

The adjacent angles of a parallelogram are in the ratio 5:4.

To find:

The measure of each of the angles of a parallelogram.

Solution:

As we know that in a parallelogram ABCD, the opposite angles are equal. This means,

angle a = angle c

and

angle b = angle d

Also,

The sum of adjacent angles of a parallelogram is equal to 180°.

This means,

angle a + angle b = 180°

angle b + angle c = 180°

angle c + angle d = 180°

angle a + angle d = 180°

Now, as given, we have,

The adjacent angles of a parallelogram are in the ratio 5:4.

Let x be the common factor in both adjacent angles.

So, the two adjacent angles are 5x and 4x.

Hence,

$5x + 4x = 180°$

$9x = 180°$

$x = 20°$

After putting the value of x = 20° in 5x and 4x, we have,

5x = 5(20) = 100°

4x = 4(20) = 80°

As opposite angles are equal, the other two angles are 100° and 80°.

Hence, the four angles of a parallelogram are 100°, 80°, 100° and 80°.