If the angles of a triangle are x,

Question:

If the angles of a triangle are x, y and 40° and the difference between

the two angles x and y is 30°. Then, find the value of x and y,

Solution:

Given that, x, y and 40° are the angles of a triangle.

x + y + 40° = 180°

[since, the sum of all the angles of a triangle is 180°]

$\Rightarrow \quad x+y=140^{\circ}$ $\ldots$ (i)

Also, $x-y=30^{\circ}$....(ii)

On adding Eqs. (i) and (ii), we get

$2 x=170^{\circ}$

$\Rightarrow \quad x=85^{\circ}$

On putting $x=85^{\circ}$ in Eq. (i), we get

$85^{\circ}+y=140^{\circ}$

$\Rightarrow$ $y=55^{\circ}$

Hence, the required values of $x$ and $y$ are $85^{\circ}$ and $55^{\circ}$, respectively.

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