Question

if two adjacent angles of a parallelogram PQRS are (10y-9)° & (8y+45°), Find all the four angles of parallelogram.

Answer 1

let one angle be a and other be b
now, a=10y -9
b= 8y + 45
now , a+ b =( 10y-9)+(8y+45)=180
sum of angles on same side of the transversal
therefore,
18y +36=180
y + 2 =10 (dividing entirely by 18 )
y =8
therefore,
a=71 and b =109
so another two angles are c=a = 71 (opposite angles of a parallelogram are equal)
similarly d=b=109

Answer 2

According to the rule
=>the sum of adjacent angle is equal to 180° in parallelogram.

so following this,

10y-9+8y+45=180

18y+36=180

18y=180-36

18y=144

y=8


the 1st angle=(10y-9)°

=(10×8-9)°

=80-9

=71°


2nd angle=(8y+45)

=8×8+45

=64+45

= 109

according to rule
=>opposite angles of parellelogram are equal.

the angle of parellelogram are

1st angle=71°

2nd angle=109°

3rd angle=71°

4th angle=109°