Question

If the sizes of the interior angles of a pentagon are 2r, 3x", 4x, 5x° and 6x, find the largest interior angle of the pentagon.

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Answer 1

$\star \; {\underline{\boxed{\orange{\pmb{\frak{ Appropriate \; Question \; :- }}}}}}$

If the Sizes of the interior angles of a pentagon are 2x° , 3x° ,4x° ,5x° and 6x° .Find the larges interior angle .

$\star \; {\underline{\boxed{\green{\pmb{\frak{ Given \; :- }}}}}}$

• ∠1 = 2x
• ∠2 = 3x
• ∠3 = 4x
• ∠4 = 5x
• ∠6 = 6x

$\star \; {\underline{\boxed{\pink{\pmb{\frak{ To \; Find \; :- }}}}}}$

• Measure of largest angle

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$\star \; {\underline{\boxed{\purple{\pmb{\frak{ SolutioN \; :- }}}}}}$

$\dag$ We know That :

$\qquad \; \; {\orange{\bigstar \; \; {\red{\underbrace{\underline{\blue{\sf{ Sum \; of \; Angles {\small_{(Pentagon)}} = 540° }}}}}}}}$

$\dag$ Calculating the Value of x :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 2x^{ \circ } + 3x^{ \circ } + 4x^{ \circ } + 5x^{ \circ } + 6x^{ \circ } = 540^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 5x^{ \circ } + 9x^{ \circ } + 6x^{ \circ } = 540^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 5x^{ \circ } + 15x^{ \circ } = 540^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 20x^{ \circ } = 540^{ \circ } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { x = \dfrac{540}{20} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { x = \cancel\dfrac{540}{20} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\red{\pmb{\frak{ x = 27 }}}}}} \bigstar \\ \\ \\ \end{gathered}$

$\dag$ Calculating the Angles :

• ∠1 = 2x = 2(27) = 54°
• ∠2 = 3x = 3(27) = 81°
• ∠3 = 4x = 4(27) = 108°
• ∠4 = 5x = 5(27) = 135°
• ∠5 = 6x = 6(27) = 162°

$\therefore \;$ The largest angle is 162° .

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