Answer:
The value of x is [tex]\boxed{\sf{{45}^{\circ}}}[/tex]
Step-by-step explanation:
Solution :
Here we have given two angles of triangle are 80⁰,55⁰.
We need to find the third angle of triangle (x).
- As we know that the sum of interior angles of triangle is 180⁰.
Now, According to the question.
[tex]{\twoheadrightarrow{\sf{ \: \: Sum \: of \: interior \: angles = {180}^{0}}}}[/tex]
[tex]{\twoheadrightarrow{\sf{ \: \: {80}^{0} + {55}^{0} + x= {180}^{0}}}}[/tex]
[tex]{\twoheadrightarrow{\sf{ \: \: {135}^{0} + x= {180}^{0}}}}[/tex]
[tex]{\twoheadrightarrow{\sf{ \: \: x= {180}^{0} - {135}^{0}}}}[/tex]
[tex]{\twoheadrightarrow{\sf{ \: \: x = {45}^{0}}}}[/tex]
[tex]\star \: \: {\underline{\boxed{\tt{\red{x = {45}^{0}}}}}}[/tex]
Hence, the value of x is 45⁰.
[tex]\begin{gathered}\end{gathered}[/tex]
Verification :
To verify, we'll add all angles of triangle and check the sum of triangle is 180⁰ or not.
[tex]{\twoheadrightarrow{\sf{ \: \: Sum \: of \: interior \: angles = {180}^{0}}}}[/tex]
[tex]{\twoheadrightarrow{\sf{ \: \: {80}^{0} + {55}^{0} + {45}^{0}= {180}^{0}}}}[/tex]
[tex]{\twoheadrightarrow{\sf{ \: \: {135}^{0} + {45}^{0}= {180}^{0}}}}[/tex]
[tex]{\twoheadrightarrow{\sf{ \: \:{180}^{0}= {180}^{0}}}}[/tex]
[tex]\star \: \: {\underline{\boxed{\tt{\red{LHS = RHS}}}}}[/tex]
Hence Verified!
[tex]\rule{300}{2.5}[/tex]
