Question

if ratio of 3 angle of triangle is 3: 4: 2: find all angle of the triangle​

Answer 1

Given that, The Ratio of three angles of a triangle is 3:4:2.

Need To find: All angles of the triangle.

❍ Let the angles of the triangle are 3x, 4x and 2x respectively.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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• Sum of all angles of the triangle is 180°.

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Therefore,

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$:\implies\sf 2x + 3x + 4x = 180^\circ \\\\\\:\implies\sf 9x = 180^\circ \\\\\\:\implies\sf x = \cancel\dfrac{180}{9}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 20^\circ}}}}}\:\bigstar$

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Hence,

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• First angle, 2x = 2(20) = 40°
• Second angle, 3x = 3(20) = 60°
• Third angle, 4x = 4(20) = 80°

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$\therefore{\underline{\sf{Hence,\; measure\;of\;all\;angles\;are\; \bf{40^\circ,60^\circ\;\&\;80^\circ }\;\sf{respectively}.}}}$

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$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: Verification \: :}}}}}\mid}$⠀

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• As We know that sum of all angles of the triangle is 180°. We've measure of all angles of the triangle. So, let's verify them;

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$:\implies\sf a + b + c = 180^\circ \\\\\\:\implies\sf 40^\circ + 60^\circ + 80^\circ = 180^\circ\\\\\\:\implies{\underline{\boxed{\sf{ 180^\circ = 180^\circ}}}}$

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$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence Verified!}}}}$

Answer 2

Given : Ratio of three angles of a triangle is 3 : 4 : 2.

To Find : All angles of the triangle.

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Put k in the ratio.

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Now, angles are -

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• First angle = 2k
• Second angle = 3k
• Third angle = 4k

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As we know that -

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Sum of all angles of a triangle is 180°.

i.e.

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$\star \: \underline{\boxed{\sf\pink{ \angle1 + \angle2 + \angle3 = 180 \degree}}}$

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$\it{\bold{\underline{According \: to \: the \: question \: : }}}$

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$\sf:\implies \: 2k + 3k + 4k = 180 \\ \\ \\ \sf:\implies \: 5k + 4k = 180 \\ \\ \\ \sf:\implies \: 9k = 180 \\ \\ \\ \sf:\implies \: k = \cancel\frac{180}{9} \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{k = 20}}} \: \bigstar \\ \\ \\ \\ \sf \therefore{ \underline{Value \: of \: k \: is \: \bold{20}.}}$

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Now, put the value of k in the ratio.

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• First angle = 2k = 2(20) = 40°
• Second angle = 3k = 3(20) = 60°
• Third angle = 4k = 4(20) = 80°

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$\sf \therefore{ \underline{Hence, \: the \: all \: angles \: of \: the \: triangle \: are \: \bold{40 \degree} \: \bold{60 \degree} \: and \: \bold{80 \degree} \: respectively.}}$