The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angle is $10^o$, find the three angles.

Given:

The angles of a triangle are arranged in ascending order of magnitude.

The difference between two consecutive angle is $10^o$.

To do:

We have to find the three angles.

Solution:

We know that,

Sum of the angles in a triangle is $180^o$.

Let the three consecutive angles be $x^o, (x+10)^o$ and $(x+20)^o$.

Therefore,

$x^o+(x+10)^o+(x+20)^o=180^o$

$3x^o+30^o=180^o$

$3x^o=180^o-30^o$

$3x^o=150^o$

$x^o=\frac{150^o}{3}$

$x^o=50^o$

$\Rightarrow (x+10)^o=(50+10)^o=60^o$

$\Rightarrow (x+20)^o=(50+20)^o=70^o$

Therefore, the three angles of the triangle are $50^o, 60^o$ and $70^o$.

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