Question

In triangle ABC, angle A =angle B/2=angle C/2 then angleA is

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{In triangle ABC}$

$\mathsf{\angle{A}=\dfrac{\angle{B}}{2}=\dfrac{\angle{C}}{2}}$

$\underline{\textbf{To find:}}$

$\mathsf{\angle{A}}$

$\underline{\textbf{Solution:}}$

$\textsf{We apply one of the important property of triangle}$

$\textsf{to solve this problem}$

$\textsf{As per given data,}$

$\mathsf{\angle{A}=\dfrac{\angle{B}}{2}=\dfrac{\angle{C}}{2}}$

$\textsf{Multiply throughout by 2}$

$\mathsf{2\,\angle{A}=\angle{B}=\angle{C}}$

$\textsf{We know that,}$

$\boxed{\textbf{Sum of all interior angles of a triangle is}\;\mathsf{180^\circ}}$

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

$\implies\mathsf{\angle{A}+2\,\angle{A}+2\,\angle{A}=180^\circ}$

$\implies\mathsf{5\,\angle{A}=180^\circ}$

$\implies\mathsf{\angle{A}=\dfrac{180^\circ}{5}}$

$\implies\boxed{\mathsf{\angle{A}=36^\circ}}$

$\underline{\textbf{Find more:}}$

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