Question

Two adjacent angles of a rhombus are in the ratio 4:5. Find the measure of all its angles

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∘/9y=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∘