In triangle PQR $\angle P = (x-1) $, $\angle Q = 4x $ and $\angle R = (2x -3 )$. Find the values of three angles.
Given :
In triangle PQR $\angle P = (x-1) $, $\angle Q = 4x $ and $\angle R = (2x -3 )$
To do :
We have to find the values of the three angles.
Solution :
Sum of all the angles of triangle is 180°.
In $\Delta PQR$,
$\angle P + \angle Q + \angle R = 180°$
$x - 1 + 4x + 2x - 3 = 180$
$ x + 2x + 4x -3 - 1 = 180$
$ 7x - 4 = 180$
$7 x = 180 + 4$
$7 x = 184$
$x = \frac{184}{7}$
$x = 26.3$
$\angle P = x - 1 = 26.3 - 1 = 25.3°$
$\angle Q = 4 x = 4 \times 26.3 = 105.2°$
$\angle R = 2 x - 3 = 2\times 26.3 - 3 = 52.6 - 3 = 49.6$
Therefore, three angles are, $\angle P = 25.3° , \angle Q = 105.2° , \angle R = 49.6°$.
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