Question

The largest angle of a triangle is equal to the sum of the other two angles. If the smallest angle is 1/3 of the largest angle then the angles of a triangle is​

Answer 1

Answer:

Under the Permanent Settlement, the rates of revenue were fixed permanently, i.e. it was not to be increased ever in future. But in the mahalwari system it was decided that the rate of revenue would be revised periodically, not permanently fixed.

Under the Permanent Settlement, the zamindars were given the charge of collecting revenue from the peasants and paying it to the Company. But in the mahalwari system this charge was given to the village headman.

Explanation:

aap bhe question mat post karo acc pe warning a raha ha pehele jaise

Answer 2

Given:

The largest angle of a triangle is equal to the sum of the other two angles. The smallest angle is 1/3 of the largest angle.

Need to Find: Angles of Triangle.

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❍ Now, let us assume that tLargest angle as x, Smallest angle as x/3 and another angle as y

1st equation :-

$\\:\implies\quad\sf{x = \dfrac{x}{3} + y}$

$\\:\implies\quad\sf{x = x +\dfrac{3y}{3}}$

$\\:\implies\quad\sf{3x = x + 3y}$

$\\:\implies\quad\sf{2x = 3y}$

$\\:\implies\quad\sf{2x - 3y = 0\qquad\qquad\left\lgroup\begin{matrix}\sf{{eq}^{n}} \: (I) \end{matrix}\right\rgroup\]}$

Now,

2nd equation :-

As we know that sum of all angles in a triangle is 180°.

$\\:\implies\quad\sf{x + x/3 +y = {180}^{o}}$

$\\:\implies\quad\sf{3x + x + 3y = {540}^{o}}$

$\\:\implies\quad\sf{4x + 3y = {540}^{o}\qquad\quad\left\lgroup\begin{matrix}\sf{{eq}^{n}} \: (II) \end{matrix}\right\rgroup\]}$

Adding equation (i) & (ii) we get

$\\:\implies\quad\sf{6x = {540}^{o}}$

$\\:\implies\quad\sf{x =\dfrac{540}{6}}$

$\\:\implies\quad\underline{\boxed{\pmb{\frak{x = {90}^{o}}}}}$

Now, putting the value of x = 90° in Equation (i) we get

$\\:\implies\quad\sf{{180}^{o} -3y = 0}$

$\\:\implies\quad\sf{-3y = {-180}^{o}}$

$\\:\implies\quad\sf{y =\dfrac{{180}^{o}}{3}}$

$\\:\implies\quad\underline{\boxed{\pmb{\frak{y = {60}^{o}}}}}$

And ,

$\\:\implies\quad\sf{Smallest\: angle =\dfrac{x}{3}}$

$\\:\implies\quad\sf{Smallest\: angle =\dfrac{90}{3}}$

$\\:\implies\quad\underline{\boxed{\pmb{\frak{Smallest\: angle={30}^{o}}}}}$

⠀

$\qquad\leadsto$ Hence, the angles of triangles are 90° , 60° & 30°.

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