Question

In triangle ABC , half the sum of measure of B and C is 50° then mangle A
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Answer 1

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

$\mathsf{In\;\triangle\,ABC,\;\dfrac{1}{2}(\angle{B}+\angle{C})=50^\circ}$

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

$\mathsf{\angle{A}}$

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

$\underline{\textbf{Concept used:}}$

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

$\mathsf{\dfrac{1}{2}(\angle{B}+\angle{C})=50^\circ}$

$\implies\mathsf{\angle{B}+\angle{C}=100^\circ}$

$\mathsf{But,}$

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

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

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

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