Question

5. (i) if all the angles of a hexagon are equal, find the measure of each angle.
(ii) if all the angles of a 14- sided figure are equal, find the measure of each angle.​

Answer 1

$\huge{ \underline{ \underline{ \mathbb{ \blue{ANSWER}}}}}$

$\pmb{(i) No. of \: sides \: of \: hexagon, n = 6}$

$\pmb{Let \: each \: angle \: be = x°}$

$\pmb{Sum \: of \: angles = 6x°}$

$\pmb{(n – 2) \times 180° = Sum \: of \: angles}$

$⇏\pmb{(6 – 2) \times 180° = 6x°}$

$⇏ \pmb{4 \times 180 = 6x}$

$⇏ \pmb{X = (4 × 180)/6}$

$\boxed{ \pmb{x = 120°}}$

$\underline{ \pmb{ each \: angle \: of \: hexagon = 120°}}$

________________________

$\pmb{(ii) No. of \: sides \: of \: polygon, n = 14}$

$\pmb{Let \: each \: angle = x°}$

$\pmb{ Sum \: of \: angles = 14x°}$

$\pmb{(n – 2) × 180° = Sum \: of \: angles \: of \: polygon}$

$⇏ \pmb{(14 – 2) × 180° = 14x}$

$⇏ \pmb{12 × 180° = 14x}$

$⇏ \pmb{x = (12 × 180)/14}$

$⇏ \pmb{x = 1080/7}$

$\boxed{ \pmb{x = (154.2/7)°}}$

Answer 2

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(i)No.ofsidesofhexagon,n=6

(i)No.ofsidesofhexagon,n=6

\pmb{Let \: each \: angle \: be = x°}

Leteachanglebe=x°

Leteachanglebe=x°

\pmb{Sum \: of \: angles = 6x°}

Sumofangles=6x°

Sumofangles=6x°

\pmb{(n – 2) \times 180° = Sum \: of \: angles}

(n–2)×180°=Sumofangles

(n–2)×180°=Sumofangles

⇏\pmb{(6 – 2) \times 180° = 6x°}⇏

(6–2)×180°=6x°

(6–2)×180°=6x°

⇏ \pmb{4 \times 180 = 6x}⇏

4×180=6x

4×180=6x

⇏ \pmb{X = (4 × 180)/6}⇏

X=(4×180)/6

X=(4×180)/6

\boxed{ \pmb{x = 120°}}

x=120°

x=120°

\underline{ \pmb{ each \: angle \: of \: hexagon = 120°}}

eachangleofhexagon=120°

eachangleofhexagon=120°