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# The angle of a triangle is in the ratio of $1:3:5$. Find the measure of each angle.

Last updated date: 25th Jun 2024
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Hint: At first, we should know the sum of all angles of a triangle. Then assuming one of the angles of the triangle be x and forming a linear equation, we can solve this problem.

Here the angle of the triangle is the ratio$1:3:5$.
Let us assume, one of the angles is $x$. And then according to the ratio of angles of triangle,
We have all angles as x, 3x, 5x.
We know the sum of all angles of a triangle is ${180^\circ}$.
So, forming the equation,
$x + 3x + 5x = {180^\circ}$
Solving it , we get
$\Rightarrow 9x = {180^\circ}$
$\Rightarrow x = {20^\circ}$
Now, we will substitute the value of x to find the other two angles.
Hence the angle taken as ‘$x$’ is $\Rightarrow {20^\circ}$
The angle taken as ‘$3x$’ is $\Rightarrow 3 \times {20^\circ} = {60^\circ}$
The angle taken as ‘$5x$’ is $\Rightarrow 5 \times {20^\circ} = {100^\circ}$
So, three angles of the triangle are, ${20^\circ}$, ${60^\circ}$ and ${100^\circ}$.

Additional Information: (1) Sum of all angles of triangle is ${180^\circ}$ i.e , if there is a triangle ABC , $\angle A + \angle B + \angle C = 180^\circ$.
(2) With the given ratio of some terms, we can get their actual values with the help of one single variable only.

Note: An important property of triangle for its three angles is that their sum total is ${180^\circ}$. Also the fundamental rule of ratio and proportions are used in the above problem. We solved this type of problem by assuming one of the angles as $x$ and further applying the different ratio as a triangle and measuring the angle. Linear equations and its solution methods are important here. Calculations should be done very attentively to avoid silly mistakes instead of having key concepts.