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Given :-

  • A triangle with all sides equal .

To Find :-

  • The value of x .

Solution :-

As we know that angles opposite to equal angles are equal . So ultimately all the angles inside the triangle would be equal to each other . Thus the triangle is a equilateral and each angle in a equilateral triangle is 60° . So ,

[tex]\sf\longrightarrow[/tex]9x - 3° = 60°

[tex]\sf\longrightarrow[/tex]9x = 60° +3°

[tex]\sf\longrightarrow[/tex]9x = 63°

[tex]\sf\longrightarrow[/tex]x = 63°/9

[tex]\sf\longrightarrow[/tex]x = 7°

Hence the required answer is 7° .

Given :

In the figure, it is given that a triangle with having all sides equal. And we know that, sum of all angles of the triangle is 180°.

⠀

To Find :

  • The value of x

⠀

Solution :

[tex] \implies \sf \:(9x - 3){}^{ \circ} + (9x - 3){}^{ \circ} + (9x - 3){}^{ \circ} = 180{}^{ \circ}\\ \\ \sf \implies \:9x - 3{}^{ \circ} + 9x - 3{}^{ \circ} + 9x - 3{}^{ \circ} = 180{}^{ \circ} \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf 9x + 9x + 9x - (3{}^{ \circ} + 3{}^{ \circ} + 3{}^{ \circ}) = 180{}^{ \circ} \: \: \: \: \: \\ \\ \implies \sf \: 27x - 9{}^{ \circ} = 180{}^{ \circ} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies27x = 180 {}^{ \circ} + 9{}^{ \circ}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies27x = 189{}^{ \circ}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \implies \: x = \frac{189{}^{ \circ}}{27} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf \: { \underline{ \boxed{ \pmb{ \mathfrak{x = 7°}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Therefore, the required value of x = 7°

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