Question

c. The measure of an angle of a parallelogram is one-eighth times than its adjacent angle. Find the measure of
all its angles.

Answer 1

Answer:

Let one angle of parallelogram=x

Adjacent angle of parallelogram=180−x

According to problem

x=

5

4

(180−x)

5x=720−4x

9x=720

x=80

o

One angle=80

o

Adjacent angle=100

o

.

Answer 2

Answer:

Let one angle be 1/8 x°

and adjacent angle be x°

by using angle sum property of quadrilateral

1/8x°+ x°+ 1/8x°+ x°=360°

(opposite angles in a ||gm are equal)

2(1/8x+ x) = 360

1/8x + x = 180

9/8 x = 180

x = (180 × 8)÷ 9

x = 160

therefore, all angles are 160°, 20° , 160°, 20°