Madhya Pradesh Police Exam Model Paper 9

Tips & Tricks
Given:
ABCD is a parallelogram
Concept used:
The Sum of adjacent angles of the parallelogram is 180°.
Calculation:
In parallelogram ABCD $\angle \mathit{A}\mathit{D}\mathit{C}+\angle \mathit{D}\mathit{C}\mathit{B}=180°$ [Adjacent angles of parallelogram]
$\Rightarrow \left(\mathit{z}\mathit{–}15\right)°+\left(2\mathit{z}\right)°=180°$
$\Rightarrow 3\mathit{z}=195°$
$\Rightarrow \mathit{z}=65°$
$\angle \mathit{B}\mathit{A}\mathit{D}+\angle \mathit{A}\mathit{D}\mathit{C}=180°$ [Adjacent angles of parallelogram]
$\Rightarrow \mathit{x}°+\left(\mathit{z}\mathit{–}15\right)°=180°$
$\Rightarrow \mathit{x}+\left(65\mathit{–}15\right)=180°$
$\Rightarrow \mathit{x}+50°=180°$
$\Rightarrow \mathit{x}=130°$
∠DAB + ∠ABC = 180° [Adjacent angles of parallelogram]
$\Rightarrow \mathit{x}°+\mathit{y}°=180°$
$\Rightarrow 130°+\mathit{y}°=180°$
$\Rightarrow \mathit{y}=50°$
∴ The value of x, y, and z are 130°, 50° and 65° respectively.