Question

Two adjacent angles of a parallelogram are (4-13) and (5-5). Find all the angles of the parallelogram.​

Answer 1

Answer:

Consider the parallelogram PQRS, From the question it is given that, The measure of two adjacent angles of a parallelogram is in the ratio 4: 5

So,∠P:∠Q=4:5

Let us assume the ∠P=4 y and ∠Q=5y

Then, we know that, ∠P+∠Q=180

∘

4y+5y=180

∘

9y=180

∘

y=180

∘

/9

y=20

∘

Therefore, ∠P=4y=4×20

∘

=80

∘

and ∠Q=5y=(5×20

∘

)=100

∘

In parallelogram opposite angles are equal,

So,∠R

∠S

=∠P=80

∘

=∠Q=100

∘

Answer 2

Step-by-step explanation:

Consider the parallelogram PQRS, From the question it is given that, The measure of two adjacent angles of a parallelogram is in the ratio 4: 5

So,∠P:∠Q=4:5

Let us assume the ∠P=4 y and ∠Q=5y

Then, we know that, ∠P+∠Q=180

∘

4y+5y=180

∘

9y=180

∘

y=180

∘

/9

y=20

∘

Therefore, ∠P=4y=4×20

∘

=80

∘

and ∠Q=5y=(5×20

∘

)=100

∘

In parallelogram opposite angles are equal,

So,∠R

∠S

=∠P=80

∘

=∠Q=100

∘