The angles of a triangle are $x, y$ and $40^{\circ}$. The difference between the two angles $x$ and $y$ is $30^{\circ}$. Find $x$ and $y$.

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Given:

The angles of a triangle are $x, y$ and $40^{\circ}$. The difference between the two angles $x$ and $y$ is $30^{\circ}$.

To do:

We have to find $x$ and $y$.

Solution:

We know that,

The sum of the angles of a triangle is $180^o$

Therefore,

$x+y+40^o=180^o$

$x+y=180^o-40^o$

$x+y=140^o$..........(i)

The difference between the two angles $x$ and $y$ is $30^{\circ}$.

This implies,

$x-y=30^o$........(ii)

Adding (i) and (ii), we get,

$2x=140^o+30^o$

$x=\frac{170^o}{2}$

$x=85^o$

$\Rightarrow y=85^o-30^o$

$y=55^o$

Hence, $x=85^o$ and $y=55^o$.

Updated on 10-Oct-2022 13:27:21