Answer:
The correct answer is option A) 55⁰.
Step-by-step explanation:
As we know that the sum of interior angles of triangle is 180⁰.
So, adding all the given sides and subtracting to 180⁰, to find the value of x.
[tex]\begin{gathered}\quad\longrightarrow{\rm{Sum \: of \: all \: angles = {180}^{\circ}}}\\\\\quad{\longrightarrow{\tt{(x + 62) + ({45}^{ \circ}) + (87 + x) = {180}^{\circ}}}}\\\\\quad{\longrightarrow{\tt{(x + x) + (62 + 45 + 87)= {180}^{\circ}}}}\\\\\quad{\longrightarrow{\tt{(2x) + (107 + 87)= {180}^{\circ}}}}\\\\\quad{\longrightarrow{\tt{(2x) + (194)= {180}^{\circ}}}}\\\\\quad{\longrightarrow{\tt{(2x)= {180} - 194}}}\\\\\quad{\longrightarrow{\tt{(2x)= - 14}}}\\\\\quad{\longrightarrow{\tt{2x= - 14}}}\\\\\quad{\longrightarrow{\tt{x= \dfrac{ - 14}{2}}}}\\\\\quad{\longrightarrow{\tt{\underline{\underline{x = - 7}}}}}\end{gathered}[/tex]
Hence, the value of x is -7.
[tex]\begin{gathered}\end{gathered}[/tex]
Now, we know the value of x. So, calculating the measurement of angle A.
[tex]\begin{gathered}\qquad{\leadsto{\tt{A = x + 62}}}\\\\\qquad{\leadsto{\tt{A = - 7 + 62}}}\\\\\qquad{\leadsto{\tt{\underline{\underline{A = {55}^{ \circ}}}}}}\end{gathered}[/tex]
Hence, the measurement of angle A is 55⁰.
[tex]\rule{300}{2.5}[/tex]
