Given:
ABCD is a parallelogram
The ratio of adjacent angles = 4 ∶ 5
Concept used:
The Sum of adjacent angles of the parallelogram is 180°.
The opposite angles of the parallelogram are always equal to each other.
Calculation:
ABCD is a parallelogram,
Let the ∠A and ∠D be 4x and 5x respectively.
∠A+∠D=180° [Adjacent angles of parallelogram]
⇒4x+5x=180° ⇒9x=180° ⇒x=20° ∠A=4x ⇒∠A=4×20° ⇒∠A=80° ∠D=5x ⇒∠D=5×20° ⇒∠D=100° ∠A = ∠C [Opposite angle of parallelogram]
∠D = ∠B [Opposite angle of parallelogram]
So,
∠A=∠C=80° ∠D=∠B=100° ∴ All angles of parallelogram is 80°, 100°, 80°, 100°.