[tex]\underline{\underline{\large\bf{Given:-}}}[/tex]
[tex]\red{\leadsto}\:[/tex][tex]\textsf{The given triangle is isosceles triangle } [/tex]
[tex]\sf with \: AB = AC [/tex]
[tex]\green{\leadsto}\:[/tex][tex]\sf m∠B = 76⁰[/tex]
[tex]\underline{\underline{\large\bf{To Find:-}}}[/tex]
[tex]\orange{\leadsto}\:[/tex][tex]\textsf{} [/tex][tex]\sf m∠A [/tex]
[tex]\\[/tex]
[tex]\underline{\underline{\large\bf{Solution:-}}}\\[/tex]
[tex]\longrightarrow[/tex]Since the given triangle is isosceles, the angle opposite to equal sides will be equal
[tex]\quad\therefore[/tex]So, m∠A = m∠C
Now,
By angle sum property of triangle,sum of all angles inside triangle = 180⁰
[tex]\begin{gathered}\\\implies\quad \sf m∠A+m∠C+ m∠B = 180⁰ \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf m∠A+m∠A+ 76 = 180⁰\quad(m∠C=m∠A) \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2m∠A = 180 -76 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2m∠A = 104 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf m∠A = \frac{104}{2} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \boxed{\sf{ m∠A = 52⁰}} \\\end{gathered} [/tex]
