Answer
405k+ views
Hint: We are given a parallelogram and we are given one angle is some fraction of its adjacent angle and we have to find all the four angles. For this first we will assume the adjacent angle as any variable and then take the angle which is given as a fraction of adjacent angles. Applying the concept of parallelogram with the sum of adjacent angles in parallelogram is ${180^\circ}$. On equating the sum of angles to ${180^\circ}$ we will get the variable and on finding the variable from it we will find the two angles and by using the concept that opposite angles of parallelogram are equal will find all the four angles.
Complete step-by-step solution:
Step1: We are given a parallelogram in which an angle is two-third of its adjacent angles.
Let’s take a parallelogram $ABCD$ in which let us assume $\angle A = x$ and $\angle B = \dfrac{{1x}}{3}$. As we know that the sum of adjacent angles is ${180^\circ}$. On forming the equation we get
$\angle A + \angle B = 180$
$x + \dfrac{{1x}}{3} = 180$
On adding the terms by taking L.C.M
$ \Rightarrow \dfrac{{3x + x}}{3} = 180$
$ \Rightarrow 4x = 180 \times 3$
On dividing by $4$
$x = \dfrac{{180 \times 3}}{4}$
On solving the equation we get
$x = {135^\circ}$
Putting the value of $x$ for $\angle B$ we get
$\angle B = \dfrac{1}{3} \times 135$
$\angle B = 45$
Step2: As we know that in parallelograms opposite angles are equal then $\angle B = \angle D$and $\angle A = \angle C$ as they form a pair of opposite angles. Hence $\angle B = \angle D = 45$ and $\angle A = \angle C = 135$
Hence four angles are $45,45,135,135$
Note: In such types of questions always draw a diagram by doing this it is quite helpful and in such questions there are small calculations only. These are properties based questions so remember and apply the concept properly. These do not require the long calculation just a right concept of properties. In such questions always take
Points to remember:
Sum of adjacent angles in parallelogram is $180$
Opposite angles are equal in a parallelogram
Complete step-by-step solution:
Step1: We are given a parallelogram in which an angle is two-third of its adjacent angles.
![seo images](https://www.vedantu.com/question-sets/6e965e36-0570-4d3c-998d-f6736d9799b29033020486803808348.png)
Let’s take a parallelogram $ABCD$ in which let us assume $\angle A = x$ and $\angle B = \dfrac{{1x}}{3}$. As we know that the sum of adjacent angles is ${180^\circ}$. On forming the equation we get
$\angle A + \angle B = 180$
$x + \dfrac{{1x}}{3} = 180$
On adding the terms by taking L.C.M
$ \Rightarrow \dfrac{{3x + x}}{3} = 180$
$ \Rightarrow 4x = 180 \times 3$
On dividing by $4$
$x = \dfrac{{180 \times 3}}{4}$
On solving the equation we get
$x = {135^\circ}$
Putting the value of $x$ for $\angle B$ we get
$\angle B = \dfrac{1}{3} \times 135$
$\angle B = 45$
Step2: As we know that in parallelograms opposite angles are equal then $\angle B = \angle D$and $\angle A = \angle C$ as they form a pair of opposite angles. Hence $\angle B = \angle D = 45$ and $\angle A = \angle C = 135$
Hence four angles are $45,45,135,135$
Note: In such types of questions always draw a diagram by doing this it is quite helpful and in such questions there are small calculations only. These are properties based questions so remember and apply the concept properly. These do not require the long calculation just a right concept of properties. In such questions always take
Points to remember:
Sum of adjacent angles in parallelogram is $180$
Opposite angles are equal in a parallelogram
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)