Question

.Sum of two consecutive angles of a parallelogram are in the ratio of 4:5. Find all angle of a parallelogram​

Answer 1

Step-by-step explanation:

Give: ABCD is a parallelogram. angle A : angle B = 4:5,AB|| CD,BC|| AD.

TO find :Another two sides of raito.

find: ABCD is a parallelogram. let's take 4:5 as 4x:5x.AB is parallel to CD ______(given)

angle Ais congruent to angle C_____(opposite side of a parallelogram is congruent)

therefore 4 x = C

similarly,

angle A is congruent to angle D_____(opposite side of parallelogram is congruent)

therefore angle D = 5x.

AD || BC___(given)

therefore angle A + angle D =angles B + angle C

4x+5x= 5x+4x

9x=9x_____(dividing both sides by 9)

x=x

therefore, x-x=0.

therefore angle A = 4, Angle B =

5, angle C=4 , angle D= 5.