
If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3 which is the smallest of the two angles?
Answer
509.4k+ views
Hint: Use the property that the sum of the two interior angles on the same side of a transversal intersecting two parallel lines is equal to $180{}^\circ $ . It is also given that the ratio of the angles is 2:3. So we can consider the smaller angle as x and express another angle y in terms of x using the ratio.
Complete step-by-step answer:
Let us start by drawing a representative diagram of the situation given in the question.
Now we know that the sum of the two interior angles on the same side of a transversal intersecting two parallel lines is equal to $180{}^\circ $ . This can be written in the form of equation as:
$x+y=180{}^\circ ..........(i)$
Also, it is given that the ration between the angles is 2:3 and now we will consider that x is the smaller angle. So, we can represent these mathematically as:
$\dfrac{x}{y}=\dfrac{2}{3}$
$\Rightarrow y=\dfrac{3}{2}x$
So, if we substitute the value of y in equation (i), we get
$x+\dfrac{3}{2}x=180{}^\circ $
$\Rightarrow \dfrac{5}{2}x=180{}^\circ $
$\Rightarrow x=72{}^\circ $
Therefore, we can conclude that the smaller angle x is equal to $72{}^\circ $ .
Note: It is very important to learn all the properties of angles formed by transversal cutting two parallel lines, as they are often used. The list of such angles include: angles on the same side of the transversal, alternate angles, corresponding angles etc. You should also be careful about the calculation part and while using the definition of ratio. We can also consider x as the bigger angle and solve, so accordingly the value of x and y would change.
Complete step-by-step answer:
Let us start by drawing a representative diagram of the situation given in the question.

Now we know that the sum of the two interior angles on the same side of a transversal intersecting two parallel lines is equal to $180{}^\circ $ . This can be written in the form of equation as:
$x+y=180{}^\circ ..........(i)$
Also, it is given that the ration between the angles is 2:3 and now we will consider that x is the smaller angle. So, we can represent these mathematically as:
$\dfrac{x}{y}=\dfrac{2}{3}$
$\Rightarrow y=\dfrac{3}{2}x$
So, if we substitute the value of y in equation (i), we get
$x+\dfrac{3}{2}x=180{}^\circ $
$\Rightarrow \dfrac{5}{2}x=180{}^\circ $
$\Rightarrow x=72{}^\circ $
Therefore, we can conclude that the smaller angle x is equal to $72{}^\circ $ .
Note: It is very important to learn all the properties of angles formed by transversal cutting two parallel lines, as they are often used. The list of such angles include: angles on the same side of the transversal, alternate angles, corresponding angles etc. You should also be careful about the calculation part and while using the definition of ratio. We can also consider x as the bigger angle and solve, so accordingly the value of x and y would change.
Recently Updated Pages
What is the tent of the Changpa tribe called A Rebo class 7 social science CBSE

Who is the President of India class 7 social science CBSE

In the given figure SRparallel QP and angle RPQ 30 class 7 maths CBSE

Describe Baburs conquest of Punjab class 7 social science CBSE

Who is incharge of all the police stations in a di class 7 social science CBSE

Fill in the blanks Every number is a multiple of class 7 maths CBSE

Trending doubts
The singular of lice is louse A Yes B No class 8 english CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

How many ounces are in 500 mL class 8 maths CBSE

Advantages and disadvantages of science

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

What led to the incident of Bloody Sunday in Russia class 8 social science CBSE
