Question
$ABCD$ is a parallelogram in which $\angle\text{A}=70^\circ$, compute $\angle\text{B},\angle\text{C}$ and $\angle\text{D}$.
✓
Answer
In parallelogram $ABCD$, $\angle\text{A}=70^\circ$ But
$\angle\text{A}+\angle\text{B}=180^\circ$ (Sum of adjacent angles)
$\Rightarrow70^\circ+\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{B}=180^\circ-70^\circ=110^\circ$$\angle\text{B}=110^\circ$ But
$\angle\text{C}=\angle\text{A}$ and $\angle\text{D}=\angle\text{B}$ (Opposite angles)
$\angle\text{C}=70^\circ$ and $\angle\text{D}=110^\circ$
Hence, $\angle\text{B}=110^\circ$
$\angle\text{C}=70^\circ$ and $\angle\text{D}=110^\circ$
$\angle\text{A}+\angle\text{B}=180^\circ$ (Sum of adjacent angles)
$\Rightarrow70^\circ+\angle\text{B}=180^\circ$
$\Rightarrow\angle\text{B}=180^\circ-70^\circ=110^\circ$$\angle\text{B}=110^\circ$ But
$\angle\text{C}=\angle\text{A}$ and $\angle\text{D}=\angle\text{B}$ (Opposite angles)
$\angle\text{C}=70^\circ$ and $\angle\text{D}=110^\circ$
Hence, $\angle\text{B}=110^\circ$
$\angle\text{C}=70^\circ$ and $\angle\text{D}=110^\circ$
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