Question

four angles of a pentagon are 123 degree 84 degree 113 degree and 96 degree calculate the fifth angle​

Answer 1

Step-by-step explanation:

180-123=57

180-84=96

180-113=67

180-96=84

now summation of external angles =360

and we have

57+96+67+84=304

now the required angle is 304.

Answer 2

Given :

• 1st angle of the Pentagon = 123°
• 2nd angle of the Pentagon = 84°
• 3rd angle of the Pentagon = 113°
• 4th angle of the Pentagon = 96°

To Find :

• 5th angle of the Pentagon = ?

Solution :

✭ We know That :

• ${\underline{\boxed{\orange{\sf{ Sum \; of \; Angles{\small_{(Pentagon)}} = 540° }}}}}$

Where :

• ➳ ∠1 = 123°
• ➳ ∠2 = 84°
• ➳ ∠3 = 113°
• ➳ ∠4 = 96°
• ➳ ∠5 = ?

$\\ \qquad{\rule{150pt}{1pt}}$

✭ Calculating the 5th Angle :

$\begin{gathered} \dashrightarrow \; \; \sf { ∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 540° } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 123° + 84° + 113° + 96° + ∠5 = 540° } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 207° + 209° + ∠5 = 540° } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { 416° + ∠5 = 540° } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { ∠5 = 540° - 416° } \\ \end{gathered}$

$\begin{gathered} {\qquad \; \; {\therefore \; {\underline{\boxed{\color{darkblue}{\pmb{\frak{ ∠5 = 124° }}}}}}}} \end{gathered}$

$\\ \qquad{\rule{150pt}{1pt}}$

✭ Therefore :

❛❛ 5th Angle of the Pentagon is 124° . ❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$