
The angle of a triangle is in the ratio of \[1:3:5\]. Find the measure of each angle.
Answer
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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.
Complete step-by-step answer:
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.
Complete step-by-step answer:
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.
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