Mathematics: What is the value of x?

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What is the value of x? - id15154766, ibrsayed6671

ashleyp2249

05.01.2022

The value of x is $\boxed{\sf{{45}^{\circ}}}$

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.

${\twoheadrightarrow{\sf{ \: \: Sum \: of \: interior \: angles = {180}^{0}}}}$

${\twoheadrightarrow{\sf{ \: \: {80}^{0} + {55}^{0} + x= {180}^{0}}}}$

${\twoheadrightarrow{\sf{ \: \: {135}^{0} + x= {180}^{0}}}}$

${\twoheadrightarrow{\sf{ \: \: x= {180}^{0} - {135}^{0}}}}$

${\twoheadrightarrow{\sf{ \: \: x = {45}^{0}}}}$

$\star \: \: {\underline{\boxed{\tt{\red{x = {45}^{0}}}}}}$

Hence, the value of x is 45⁰.

$\begin{gathered}\end{gathered}$

Verification :

To verify, we'll add all angles of triangle and check the sum of triangle is 180⁰ or not.

${\twoheadrightarrow{\sf{ \: \: Sum \: of \: interior \: angles = {180}^{0}}}}$

${\twoheadrightarrow{\sf{ \: \: {80}^{0} + {55}^{0} + {45}^{0}= {180}^{0}}}}$

${\twoheadrightarrow{\sf{ \: \: {135}^{0} + {45}^{0}= {180}^{0}}}}$

${\twoheadrightarrow{\sf{ \: \:{180}^{0}= {180}^{0}}}}$

$\star \: \: {\underline{\boxed{\tt{\red{LHS = RHS}}}}}$

Hence Verified!

$\rule{300}{2.5}$

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