Question

if three angles of the triangle are in the ratio 2:2:5 find the measure of the greatest angle


please give the answer with full formula​

Answer 1

Given :-

• The angles of a triangle are in the ratio of 2:2:5.

To Find :-

• Find the measure of greatest angle of the triangle

Solution :-

~Here, we’re given the ratio of angles of a triangle and we need to find measure of each angle. We can form an equation according to the given ratios and the angle sum property of a triangle. By solving that equation we can find the measure of each angle of this triangle.

_____________

As we know that ,

★ According to the angle sum property of triangles sum of all angles of a triangle is 180°.  

Assuming angles of the triangle

• First angle = 2x  
• Second angle = 2x  
• Third angle = 5x  

Solving the equation :-

⟶ 2x + 2x + 5x = 180  

⟶ 9x = 180  

⟶ x = 180/9  

⟶ x = 20  

∴ First angle = 40°  

 Second angle = 40°

 Third angle = 100°  

_____________

Hence,  

• Measure of greatest angle is 100°

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Answer 2

Answer:

${\bigstar{\underline{\underline{\pmb{\sf{\blue{Given : }}}}}}}$

• ● Three angles are in ratio 2:2:5

${\bigstar{\underline{\underline{\pmb{\sf{\blue{To \: Find : }}}}}}}$

• ● All three angles
• ● Measurement of greatest amgle.

${\bigstar{\underline{\underline{\pmb{\sf{\blue{Solution: }}}}}}}$

$\dag{\small{\bf{Let ,The \: angles}}}$

• ● 2x
• ● 2x
• ● 5x

$\dag \small\bf{Finding \: The \: Angles }$

As we know that the measurement of three angles of triangle is 180⁰.(A+B+C=18⁰)

So,

$:\implies{\sf{2x + 2x + 5x = \bf{180}^{\circ}}}$

$:\implies{\sf{9x =\bf{180}^{\circ}}}$

$:\implies{\sf{x}={\bf\dfrac{180}{9}}}$

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

$: \implies \sf{x = \bf{20}^{\circ}}$

${\bigstar{\underline{\boxed{\pmb{\sf{\pink{x= {20}^{\circ}}}}}}}}$

$\dag\bf{Angles}$

• ● A = 2×20⁰ = 40⁰
• ● B = 2× 20⁰ = 40⁰
• ● C = 5×20⁰ = 100⁰

${\bigstar{\underline{\underline{\pmb{\sf{\blue{Verification: }}}}}}}$

$\dag\bf{Checking \: our \: answer }$

As we know that the measurement of three angles of triangle is 180⁰.(A+B+C=18⁰)

So,

${: \implies \sf{40}^{\circ} + {40}^{\circ} + {100}^{\circ} = \bf{180}^{\circ} }$

${: \implies\sf{180}^{\circ}= \bf{180}^{\circ} }$

${\dag{\underline{\boxed{\pmb{\sf{\pink{LHS=RHS}}}}}}}$

● Hence Verified..

${\bigstar{\underline{\underline{\pmb{\sf{\blue{Therefore: }}}}}}}$

● The largest angle is 100⁰.