Question

If the angles of a triangle are (x -10°) , (2x + 10°) and 6x , what is the value of x?​

Answer 1

$\bold{\underline{\mathfrak{ \bigstar \: Answer \: -}}}$

• The value of x = 20.

$\bold{\underline{\mathfrak{ \bigstar \: To \: find \: -}}}$

• The value of x.

$\bold{\underline{ \mathfrak{ \bigstar \: Step\!-\!by\!-\!step \: explanation \: -}}}$

• Here, the angles of a triangle (with a variable) are given to us. We have to find the value of x. Let's use the angle sum property of triangles to solve this question!

Angle Sum Property -

$\bigstar \: \underline{ \boxed{ \sf Sum \: of \: all \: angles_{(triangle)} = 180^{\circ}}}$

Here -

• The angles are (x - 10)°, (2x + 10)° and (6x)°.

Therefore -

$\longmapsto \sf x - 10 + 2x + 10 + 6x = 180$

$\longmapsto \sf x - 10 + 2x + 10 + 6x = 180$

$\sf \longmapsto9x = 180$

$\longmapsto \sf x = \cancel{\dfrac{180}{9} }$

$\longmapsto \underline{ \boxed{ \sf x = 20}} \: \bigstar$

Thus -

• The value of x = 20.

________________________________

And the angles of the triangle are -

$\tt \mapsto (x - 10)^{\circ} = (20 - 10)^{\circ} = 10^{ \circ}$

$\mapsto \tt (2x + 10)^{\circ} = (2 \times 20 + 10)^{\circ} = 50^{ \circ}$

$\tt \mapsto (6x)^{\circ} = (6 \times 20)^{\circ} = 120^{ \circ}$

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Answer 2

$\red\bigstar$${\large{\underline{\underline{\bf{Question :-}}}}}$

• If the angles of a triangle are (x -10°) , (2x + 10°) and 6x , what is the value of x?

$\red\bigstar$${\large{\underline{\underline{\bf{Answer :-}}}}}$

• x = 20°

$\red\bigstar$${\large{\underline{\underline{\bf{Given :-}}}}}$

• ★Angles of triangle :-
• ➼(x - 10°)
• ➼(2x + 10°)
• ➼6x
• ➼ $\sf\red{Sum \: of \: all \: angles \: of \: Triangle \: = \: 180°}$

$\red\bigstar$${\large{\underline{\underline{\bf{Solution :-}}}}}$

$\sf\hookrightarrow\bold{(x - 10°) \: + \: (2x + 10°) \: + \: 6x \: = \: 180°}$

$\sf\hookrightarrow\bold{(x \: + \: 2x \: + 6x) \: + \: (-10° \: + \: 10°) \: = \: 180°}$

$\sf\hookrightarrow\bold{9x \: + \: 0 \: = \: 180°}$

$\sf\hookrightarrow\bold{9x \: = \: 180°}$

$\sf\hookrightarrow\bold{ x \: = \: \cancel\dfrac{180°}{9}}$

$\sf\hookrightarrow\bold{ x \: = \: 20°}$

• Thus , the value of x is 20°

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★ And the angles of the triangle are :-

• ➼ ( x - 10°) = 20° - 10° = 10°
• Angle (x - 10°) = 10°
• ➼ (2x + 10°) = 40° - 10° = 30°
• Angle (2x + 10°) = 30°
• ➼ 6x = 6 × 20° = 120°
• Angle 6x = 120°

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