Question

ABCD is a parallelogram. If ∠B = 1000 , then ( ∠A + ∠C ) is equal to

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Answer 1

$\textbf{Given:}$

$\textsf{In parallelogram ABCD,}$

$\mathsf{\angle{B}=100^\circ}$

$\textbf{To find:}$

$\mathsf{\angle{A}+\angle{C}}$

$\textbf{Solution:}$

$\textbf{Concept used:}$

$\boxed{\begin{minipage}{10cm} \\\textsf{1.Opposite angles of a parallelogram are equal}\\\\\textsf{2. Adjacent angles of a parallelogram are supplementary}\\ \end{minipage}}$

$\mathsf{Consider,}$

$\textsf{Using above property(2), we get}$

$\mathsf{\angle{A}+\angle{B}=180^\circ}$

$\mathsf{\angle{A}+100^\circ=180^\circ}$

$\mathsf{\angle{A}=180^\circ-100^\circ}$

$\implies\boxed{\mathsf{\angle{A}=80^\circ}}$

$\textsf{Using property(1), we get}$

$\mathsf{\angle{A}=\angle{C}}$

$\implies\boxed{\mathsf{\angle{C}=80^\circ}}$

$\mathsf{Now,}$

$\mathsf{\angle{A}+\angle{C}=80^\circ+80^\circ}$

$\implies\boxed{\mathsf{\angle{A}+\angle{C}=160^\circ}}$

$\textbf{Find more:}$