Question

in a triangle two angles are in ratio 5:8 and the third angle is is 120 degree find the other two angles​

Answer 1

let the angles be 5x and 8x

third angle = 120°

according to the question

5x+8x+120°= 180° (sum of all angles of equilateral triangle)

=> 13x+120°=180°

=> 13x= 180°-120°

=> 13x= 60°

=> x= 60/13

5x = 60/13 x 5 = 300/13 = 23.07(approx)

8x = 60/13 x 8 = 480/13 = 36.93(approx)

Hope it helps you.

Answer 2

$\setlength{\unitlength}{1.1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\qbezier(4.7,0.5)(4.4,0.25)(4.5,0)\qbezier(1.4,0.5)(1.7,0.25)(1.5,0)\qbezier(2.7,2.5)(2.9,2.3)(3.3,2.5)\put(4,0.3){ \sf 8x }\put(1.8,0.3){ \sf 120^\circ }\put(2.9,2){ \sf 5x }\end{picture}$

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☯ Let the other angles of triangle be 5x and 8x.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━

$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

Sum of all angles of a triangle is 180°.

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$\bigstar\:{\underline{\sf According\;to\;the\;question\::}}$

$:\implies\sf \angle\:A + \angle\:B + \angle\:C = 180^\circ$

$:\implies\sf 5x + 8x + 120^\circ = 180^\circ$

$\sf Here \begin{cases} & \sf{\angle\:A = \bf{5x}} \\ & \sf{\angle\:B = \bf{8x}} \\ & \sf{\angle\:C = \bf{120^\circ}}\end{cases}$

$:\implies\sf 13x + 120^\circ = 180^\circ$

$:\implies\sf 13x = 180^\circ - 120^\circ$

$:\implies\sf 13x = 60^\circ$

$:\implies\sf x = \cancel{ \dfrac{60^\circ}{13}}$

$:\implies{\underline{\boxed{\sf{\purple{x ≈ 4.6^\circ}}}}}\;\bigstar$

Therefore,

$\sf First\: angle, \:5x = 5 \times 4.6^\circ ≈ \bf{23^\circ}$

$\sf Second\: angle, \:8x = 8 \times 4.6^\circ ≈ \bf{36.8^\circ}$

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$\therefore\;{\underline{\sf{Hence,\;other\;two\;angles\;of\;triangle\;are\; \bf{23^\circ\;and\;36.8^\circ}.}}}$