Question

What is the measure of each angle of a regular hexagon ?​

Answer 1

Answer:

A hexagon has six sides, and we can use the formula degrees = (# of sides – 2) * 180. Then degrees = (6 – 2) * 180 = 720 degrees. Each angle is 720/6 = 120 degrees.

Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• What is the measure of each angle of a regular hexagon ?

$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

Let the Measure of each interior angle be $\bf{ \boxed{x°}}$

Then, The Measure of each external angle is ${\boxed {6 \times \: ( 180 \: - \: x)}}$

$\underbrace\red{\boxed{ \sf \blue{ the \: sum \: of \: the \: measures \: all \: exterior \: angles \: of \: a \: polygon \: is \: 360°}}}$

$\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\: to \:the\: Situation :}} \\\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\bf{ 6 \: \times \: ( \: 180 \: - \: x \: ) \: = \: 360 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \: 180 \: - \: x \: = \: \frac{360}{6} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \: 180 \: - \: x \: = \:\cancel \purple{ \frac{360}{6} } }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \: 180 \: - \: x \: = \: 60 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \: 180 \: - \: 60\: = \: x}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \: 120\: = \: x}}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ \:x \: = \: 120° }}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Measure \: of \: each \: angle \: of \: a \: Regular \:Hexagon \: = \underline {\underline{ 120°}}}\\\end{gathered}\end{gathered}$

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More For Knowledge:-

$\underbrace\green{\boxed{ \sf \orange{ Number \: of \: Sides \: of \: Different \: Polygon}}}$

• Triangle = 3 sides
• Quadrilateral = 4 sides
• Pentagon = 5 sides
• Hexagon = 6 sides
• Heptagon = 7 sides
• Octagon = 8 sides
• Nonagon = 9 sides
• Decagon = 10 sides

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