Madhya Pradesh Police Exam Model Paper 3

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.
$\angle \mathit{A}+\angle \mathit{D}=180°$ [Adjacent angles of parallelogram]
$\Rightarrow 4\mathit{x}+5\mathit{x}=180°$
$\Rightarrow 9\mathit{x}=180°$
$\Rightarrow \mathit{x}=20°$
$\angle \mathit{A}=4\mathit{x}$
$\Rightarrow \angle \mathit{A}=4\times 20°$
$\Rightarrow \angle \mathit{A}=80°$
$\angle \mathit{D}=5\mathit{x}$
$\Rightarrow \angle \mathit{D}=5\times 20°$
$\Rightarrow \angle \mathit{D}=100°$
∠A = ∠C [Opposite angle of parallelogram]
∠D = ∠B [Opposite angle of parallelogram]
So,
$\angle \mathit{A}=\angle \mathit{C}=80°$
$\angle \mathit{D}=\angle \mathit{B}=100°$
∴ All angles of parallelogram is 80°, 100°, 80°, 100°.