Question

Two angles of a triangle are in the ratio2:3 and its third angle is70 degree .Find other two

angles of the triangle​ please give step by step

Answer 1

$\setlength{\unitlength}{1.1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\qbezier(4.7,0.5)(4.4,0.25)(4.5,0)\qbezier(1.4,0.5)(1.7,0.25)(1.5,0)\qbezier(2.7,2.5)(2.9,2.3)(3.3,2.5)\put(4,0.3){ \sf 3x }\put(1.8,0.3){ \sf 70^\circ }\put(2.9,2){ \sf 2x }\end{picture}$

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☯ Let the other angles of triangle be 2x and 3x.

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

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

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

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

$:\implies\sf 2x + 3x + 70^\circ = 180^\circ$

$\sf Here \begin{cases} & \sf{\angle\:A = \bf{2x}} \\ & \sf{\angle\:B = \bf{3x}} \\ & \sf{\angle\:C = \bf{70^\circ}}\end{cases}$

$:\implies\sf 5x + 70^\circ = 180^\circ$

$:\implies\sf 5x = 180^\circ - 70^\circ$

$:\implies\sf 5x = 110^\circ$

$:\implies\sf x = \cancel{ \dfrac{110^\circ}{5}}$

$:\implies{\underline{\boxed{\sf{\purple{x = 22^\circ}}}}}\;\bigstar$

Therefore,

• $\sf First\: angle, \:2x = 2 \times 22^\circ = \bf{44^\circ}$
• $\sf Second\: angle, \:3x = 3 \times 22^\circ = \bf{66^\circ}$

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$\therefore\;{\underline{\sf{Hence,\;other\;two\;angles\;of\;triangle\;are\; \bf{44^\circ\;and\;66^\circ}.}}}$

Answer 2

Answer:

Given :-

• Two angles of a triangle are in the ratio of 2:3 and its third angle is 70°.

To Find :-

• What is the two angles of the triangle.

Solution :-

Let, the first angle be 2x

And, the second angle be 3x

Hence, the three angle will be 2x, 3x and 70°

We know that,

$\boxed{\bold{\small{Sum\: of\: all\: angles\: of\: a\: triangle\: =\: 180°}}}$

According to the question by using the formula we get,

⇒ 2x + 3x + 70° = 180°

⇒ 5x = 180 - 70°

⇒ 5x = 110°

⇒ x = $\dfrac{\cancel{110°}}{\cancel{5}}$

➠ x = 22°

Hence, the required angles will be,

● First angle = 2x = 2 × 22° = 44°

● Second angle = 3x = 3 × 22° = 66°

$\therefore$ The two other angles of the triangle is 44° and 66° respectively.