Question

(i) If the angle of a parallelogram is two third its adjacent angle, find the angles of the parallelogram.
(ii) Find the measure of each angle of a parallelogram if one of its angle is 30° less than twice the smallest angle​

Answer 1

Step-by-step explanation:

i)

let adjacent angle be 'x' and other angle be 'y'

then, y = (2/3) × x

by parallelogram property,

sum of adjacent angles = 180°

x + y = 180°

x + (2/3) × x = 180

x × ( 1+2/3) = 180

x × (5/3) = 180

x = 180 × 3 / 5 = 108°, opposite angle will also be 108°

y = (2/3) × x = (2/3) × 108 = 72°, opposite angle = 72°

angles = 108°, 72°, 108°, 72°

ii)

let smallest angles be ' x '

other angle = 2x - 30

by parallelogram property,

sum of adjacent angles = 180°

x + 2x - 30 = 180

3x = 180 + 30 = 210

x = 210/3 = 70°

2x - 30 = 2 × 70 - 30 = 110°

then angles are 70°, 110°, 70°, 110°