Question

The sum of angles of a triangle is 180 degree. The ratio of the angles is 2:2:5. Find the angles of the triangle.​

Answer 1

$\huge{\sf{Question:-}}$

The sum of angles of a triangle is 180 degree. The ratio of the angles is 2:2:5. Find the angles of the triangle.

$\huge{\sf{Given:-}}$

↦$\sf Sum \:of \:angle\: of \triangle = 180°$

↦Ratio of triangles 2:2:5

We know that sum of angles of triangle is 180°.

Let the angles be 2x ,2x and 5x.

$\huge{\boxed {\underline{\sf Solution:-}}}$

→ 2x + 2x + 5x= 180°

→ 9x =180°

→$x=\frac{180}{9}$

→x=20°

Therefore the angles are:-

• 2x =2×20=40°
• 2x=2×20=40°
• 5x=5×20=100°

Answer 2

Given : The sum of angles of a triangle is 180 ⁰ and The ratio of the angles is 2:2:5.

Need To Find : The measures of angles of triangle.

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$\qquad \qquad \quad \sf{\bf{ Solution \:of\:Question \::}}$ Let's Assume the measure of three angles of triangle be 2x , 2x and 5x .

$\qquad \quad \qquad \implies {\underline {\mathrm{\red {The \:sum\;of\:angles \:of\:Triangle \:is\:180\degree} }}}$

Or,

$\qquad \quad \qquad\implies {\underline {\mathrm {\red{\angle \:A + \angle\:B + \angle\:C = 180\degree}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀As , We have Assumed the measures of three angles of triangle [ $\angle\: A$ or First Angle = 2x , $\angle\: B$ or Second Angle = 2x and $\angle\: C$ or Third Angle = 5x ] and Given that the sum of the angles of triangle is 180⁰ . By Substituting the Assumed and Given values in Formula We can Find the measure of all three angles of triangle.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\underline {\bf{\star{ Now,\:By\:Substituting \:the\;Values,\:}}}$

⠀⠀⠀⠀$\sf{\implies {2x + 2x + 5x = 180\degree }}$

⠀⠀⠀⠀⠀⠀$\sf{\implies {4x + 5x = 180\degree }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\sf{\implies {9x = 180\degree }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\sf{\implies {x = \dfrac{\cancel {180}}{\cancel {9}} }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\underline{\boxed{\sf{\pink {x = 20\degree }}}}$

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⠀⠀⠀⠀⠀⠀⠀⠀⠀$\underline {\bf{\star{ Now,\:By\:Substituting \:the\;Values\:of\:x\:in\:Assumed\:angles,\:}}}$

⠀⠀⠀⠀ $\angle \: A$ or First Angle = 2x = 2 × 20 = 40 ⁰

⠀⠀⠀⠀ $\angle \: B$ or Second Angle = 2x = 2 × 9 = 40⁰

⠀⠀⠀⠀ $\angle\: C$ or Third Angle = 5x = 20 × 5 = 100⁰

$\underline {\sf{\pink{Hence,\:The\:measures \:of\:angle \:of\:triangle \:are \:40\degree , \:40\degree \: and\; 100\degree \:respectively \:.}}}$

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$\large{\bf{\mathrm { Verification \::}}}$

As , We know that ,

⠀⠀⠀⠀$\sf{\implies {L.H.S = 180\degree }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\underline {\bf{\star{ Now,\:By\:Finding \:the\;Values\:of\:R.H.S,\:}}}$

⠀⠀⠀⠀$\sf{\implies {R.H.S = 40 + 40 + 100 }}$

⠀⠀⠀⠀⠀⠀$\sf{\implies {R.H.S = 80 + 100 }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\sf{\implies { R.H.S = 180\degree }}$

Therefore,

⠀⠀⠀⠀⠀⠀⠀$\sf{\implies{\bf { L.H.S = R.H.S }}}$

⠀⠀⠀⠀⠀⠀⠀$\dag\:\:\:{\sf{\implies{\bf { Hence, \; Verified\: ! }}}}$

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