Answer
Verified
394.8k+ views
Hint: You know that the sum of angles of a triangle is ${180^ \circ }$. And if angles are given in ratio like $\angle A:\angle B:\angle C = 1:3:5$ you can write as
$\angle A = x,\angle B = 3x,\angle C = 5x$ and use the sum of angles $ = {180^ \circ }$, you will get the answer.
Complete step-by-step answer:
So, basically, the question is saying that there is a triangle whose angles are in ratio $1:3:5$. And now we have to find each angle.
So first of all, let us assume that $ABC$ is a triangle.
Now, it is given that angles are in ratio $1:3:5$
So, we can write $\angle A,\angle B,\angle C$ as the angles of $\vartriangle ABC$.
Now according to question, it is given that
$\angle A:\angle B:\angle C = 1:3:5$
As we know that if we remove the proportionality sign we must multiply by a constant.
Let $x$ be the constant
Then we can say that
$
\angle A = 1 \times x \\
\angle B = 3 \times x \\
\angle C = 5 \times x \\
$
So, we get all three angle in terms of $x$
That is, $\angle A = x,\angle B = 3x,\angle C = 5x$
So as we all know that the sum of angles of a triangle is ${180^ \circ }$.
i.e. $\angle A + \angle B + \angle C = {180^ \circ }$
Here we put the value of all three angles , we will get
$
x + 3x + 5x = 180 \\
9x = 180 \\
x = {20^ \circ } \\
$
So now we can easily find the values of all the angles.
$
\angle A = x = {20^ \circ } \\
\angle B = 3x = 3 \times 20 = {60^ \circ } \\
\angle C = 5x = 5 \times 20 = {100^ \circ } \\
$
(As we know that $\angle A = x,\angle B = 3x,\angle C = 5x$)
Hence, ${20^ \circ },{60^ \circ },{100^ \circ }$ are the angles of the triangle.
Note: As it is given that $a:b$ it means $\dfrac{a}{b}$. So in this question, $\angle A:\angle B:\angle C = 1:3:5$.
This means, $\dfrac{{\angle A}}{{\angle B}} = \dfrac{1}{3},\dfrac{{\angle B}}{{\angle C}} = \dfrac{3}{5}$
So, $
\angle A = x \\
\angle B = 3x \\
\angle C = \dfrac{5}{3}\angle B \\
$
That is, $\angle C = \dfrac{5}{3} \times 3x = 5x$
Then we put in the equation of $\vartriangle ABC$
$\angle A + \angle B + \angle C = {180^ \circ }$
And we will get the required answer.
$\angle A = x,\angle B = 3x,\angle C = 5x$ and use the sum of angles $ = {180^ \circ }$, you will get the answer.
Complete step-by-step answer:
So, basically, the question is saying that there is a triangle whose angles are in ratio $1:3:5$. And now we have to find each angle.
So first of all, let us assume that $ABC$ is a triangle.
Now, it is given that angles are in ratio $1:3:5$
So, we can write $\angle A,\angle B,\angle C$ as the angles of $\vartriangle ABC$.
Now according to question, it is given that
$\angle A:\angle B:\angle C = 1:3:5$
As we know that if we remove the proportionality sign we must multiply by a constant.
Let $x$ be the constant
Then we can say that
$
\angle A = 1 \times x \\
\angle B = 3 \times x \\
\angle C = 5 \times x \\
$
So, we get all three angle in terms of $x$
That is, $\angle A = x,\angle B = 3x,\angle C = 5x$
So as we all know that the sum of angles of a triangle is ${180^ \circ }$.
i.e. $\angle A + \angle B + \angle C = {180^ \circ }$
Here we put the value of all three angles , we will get
$
x + 3x + 5x = 180 \\
9x = 180 \\
x = {20^ \circ } \\
$
So now we can easily find the values of all the angles.
$
\angle A = x = {20^ \circ } \\
\angle B = 3x = 3 \times 20 = {60^ \circ } \\
\angle C = 5x = 5 \times 20 = {100^ \circ } \\
$
(As we know that $\angle A = x,\angle B = 3x,\angle C = 5x$)
Hence, ${20^ \circ },{60^ \circ },{100^ \circ }$ are the angles of the triangle.
Note: As it is given that $a:b$ it means $\dfrac{a}{b}$. So in this question, $\angle A:\angle B:\angle C = 1:3:5$.
This means, $\dfrac{{\angle A}}{{\angle B}} = \dfrac{1}{3},\dfrac{{\angle B}}{{\angle C}} = \dfrac{3}{5}$
So, $
\angle A = x \\
\angle B = 3x \\
\angle C = \dfrac{5}{3}\angle B \\
$
That is, $\angle C = \dfrac{5}{3} \times 3x = 5x$
Then we put in the equation of $\vartriangle ABC$
$\angle A + \angle B + \angle C = {180^ \circ }$
And we will get the required answer.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
State the differences between manure and fertilize class 8 biology CBSE
Why are xylem and phloem called complex tissues aBoth class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
What would happen if plasma membrane ruptures or breaks class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What precautions do you take while observing the nucleus class 11 biology CBSE
What would happen to the life of a cell if there was class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE