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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