Question

find the value of x in the given figure .



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Answer 1

Answer:

sum of angle of hexagon is 720⁰...

so x is equal to 45⁰

• hope it helps you
• plz mark me brainliest

Answer 2

Given :

• Measure of the angles of a hexagon :-
• First angle = x°
• Second angle = 3x°
• Third angle = 2x°
• Fourth angle = 3x°
• Fifth angle = 90°
• Sixth angle = 5x°

To find :

• The value of x

Concept :

The given figure is a hexagon as it has 6 angles, 6 sides. So, to find the value of x.. add all the angles of hexagon and keep them equal to the sum of interior angles of hexagon.

To find the sum of interior angles of any polygon, use the formula :-

• Sum of interior angles of polygon = (2n - 4) × 90°

where,

• n = number of sides

Solution :

Hexagon has six sides.

∴ Number of sides (n) = 6

$\\ \twoheadrightarrow \quad \sf x^{\circ} + 3x^{\circ} + 2x^{\circ} + 3x^{\circ} + 90^{\circ} + 5x^{\circ} = (2n - 4) \times 90^{\circ}$

$\\ \twoheadrightarrow \quad \sf x^{\circ} + 3x^{\circ} + 2x^{\circ} + 3x^{\circ} + 90^{\circ} + 5x^{\circ} = ((2 \times 6)- 4) \times 90^{\circ}$

$\\ \twoheadrightarrow \quad \sf 14x^{\circ} + 90^{\circ} = ((2 \times 6)- 4) \times 90^{\circ}$

$\\ \twoheadrightarrow \quad \sf 14x^{\circ} + 90^{\circ} = (12- 4) \times 90^{\circ}$

$\\ \twoheadrightarrow \quad \sf 14x^{\circ} + 90^{\circ} = 8 \times 90^{\circ}$

$\\ \twoheadrightarrow \quad \sf 14x^{\circ} + 90^{\circ} = 720^{\circ}$

$\\ \twoheadrightarrow \quad \sf 14x^{\circ} = 720^{\circ} - 90^{\circ}$

$\\ \twoheadrightarrow \quad \sf 14x^{\circ} = 630^{\circ}$

$\\ \twoheadrightarrow \quad \sf x = \dfrac{630^{\circ}}{14^{\circ}}$

$\\ \twoheadrightarrow \quad \sf x = \dfrac{ \not630^{\circ}}{ \not14^{\circ}}$

$\\ \twoheadrightarrow \quad \sf x = \dfrac{315^{\circ}}{7^{\circ}}$

$\\ \twoheadrightarrow \quad \sf x = \dfrac{ \not315^{\circ}}{ \not7^{\circ}}$

$\\ \twoheadrightarrow \quad \sf x = 45$

$\\ \underline{{\tiny \maltese} \quad \tt The \: value \: of \: x = 45^{\circ}}$

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VERIFICATION ::

For verifying the value of x substitute its value in the angles of hexagon if they sum upto 720° which is the sum of angles of hexagon, then the value of x is right.

• First angle = x° = 45°
• Second angle = 3x° = 3 × 45° = 135°
• Third angle = 2x° = 2 × 45° = 90°
• Fourth angle = 3x° = 3 × 45° = 135°
• Fifth angle = 90°
• Sixth angle = 5x° = 5 × 45° = 225°

Add all the angles of hexagon.

$\\ \longrightarrow \sf \quad 45^{\circ} + 135^{\circ} + 90^{\circ} + 135^{\circ} + 90^{\circ} + 225^{\circ}$

$\\ \longrightarrow \sf \quad {720}^{\circ}$

★ Sum of angles of hexagon = 720°.

HENCE, VERIFIED.