Question

angles of a triangle in which the biggest angle is double the smallest and the third angle is half the sum of other two angles.find the angle​

Answer 1

$\textbf {\underline {\underline {Step-By-Step\:Explanation}}}$

$\textbf\blue{Given:}$

• Biggest angle is double the smallest
• Third angle is half the sum of other two angles

$\textbf\blue {To\:Find:}$

• All the angles of given triangle

$\huge\underline\green {\tt Solution:}$

Let the smallest angle be ' P '

So, biggest angle will be : ' 2P '

Third angle will be : ( 2P + P ) × $\dfrac {1}{2}$

= ( 2P + P ) × 0.5

We know that the sum of all angles of a triangle is 180°

Now,

P + 2P + ( 2P + P ) 0.5 = 180°

➡ P + 2P + P + 0.5P = 180°

➡ 4P + 0.5P = 180°

➡ 4.5P = 180°

➡ P = $\dfrac {180}{4.5}$

➡ P = $\dfrac {1800}{45}$

•°• P = 40

Hence,

The smallest angle is 40°

Largest angle is 2 × 40° = 80°

Middle angle = ( 40 + 80 ) × 0.5

= 120 × 0.5

= 60°

➡ $\huge\mathscr\green {Verification:}$

• Sum of all angles of triangle is 180°

so,

40° + 80° + 60° = 180°

➡ 120° + 60° = 180°

➡ 180° = 180°

L.H.S = R.H.S

Hence, verified!

Answer 2

Answer:

40° , 80° and 60°

Step-by-step explanation:

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