What is the value of x?

Question

asked Nov 22, 2023 30.4k views

1 Answer

Kuzyn · Answer 1 · 2023-11-29T05:39:52+0000

Answer:

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

Explanation:

Here we have given two angles of triangle are 80⁰,55⁰.

We need to find the third angle of triangle (x).

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.

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

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!

$\rule{300}{2.5}$