# In a rectangle XYWZ, suppose O is the point of intersection of its diagonals if $\angle {\text{ZOW}}$ is $110^o$, then calculate the value of $\angle {\text{OYW}}$.

Last updated date: 20th Mar 2023

•

Total views: 304.8k

•

Views today: 3.83k

Answer

Verified

304.8k+ views

Hint: In order to solve this problem draw a diagram according to the question then use the concept of vertically opposite angles and sum of angles in one round is 360 degrees knowing these two things will solve this problem.

Complete step-by-step answer:

The rectangle XYWZ can be drawn as:

It is given that $\angle {\text{ZOW}}$ is 110 degrees.

We need to find $\angle {\text{OYW}}$.

We know $\angle {\text{YOW}}$+$\angle {\text{OYW}}$+$\angle {\text{OWY}}$= $180^o$ (sum of all three angles in a triangle is 180)

And we can say $\angle {\text{OYW}}$= $\angle {\text{OWY}}$ (Since In triangle OYW sides OY = OW because diagonals of rectangle bisect each other and the lengths of diagonal of rectangle are equal so we know that if the sides are equal in a triangle then angles will be equal)

So the equation becomes $\angle {\text{WOY}}$+2$\angle {\text{OYW}}$= $180^o$ ……(1)

And we know the sum of angles is one round and equals 360 degrees.

So we can say $\angle {\text{XOZ}}$+$\angle {\text{XOY}}$+$\angle {\text{YOW}}$+$\angle {\text{ZOW}}$=360 …..(2)

We can say $\angle {\text{XOZ}}$=$\angle {\text{YOW}}$ (vertically opposite angles)

And also $\angle {\text{XOY}}$= $\angle {\text{ZOW}}$=$110^o$ (given) (vertically opposite angles)

On putting the values in equation 2 we get the value of equation as:

220+2$\angle {\text{YOW}}$=360

$\angle {\text{YOW}}$=$\dfrac{{140}}{2} = 70$

On putting this value in equation 1 we get the equation as:

70+2$\angle {\text{OYW}}$=180

2$\angle {\text{OYW}}$=110

$\angle {\text{OYW}}$=$\dfrac{{110}}{2} = 55^o$

Hence the value of the angle is 55 degrees i.e. $55^o$.

Note: Whenever you face such types of problems drawing diagrams will help you to visualize and solve the problem and will make it a bit easier. Here in this problem we have used the concepts used in angles in triangles like vertically opposite angles and sum of angles in one round is 360 degrees, sum of all three angles in a triangle is 180. Using these concepts will solve this problem.

Complete step-by-step answer:

The rectangle XYWZ can be drawn as:

It is given that $\angle {\text{ZOW}}$ is 110 degrees.

We need to find $\angle {\text{OYW}}$.

We know $\angle {\text{YOW}}$+$\angle {\text{OYW}}$+$\angle {\text{OWY}}$= $180^o$ (sum of all three angles in a triangle is 180)

And we can say $\angle {\text{OYW}}$= $\angle {\text{OWY}}$ (Since In triangle OYW sides OY = OW because diagonals of rectangle bisect each other and the lengths of diagonal of rectangle are equal so we know that if the sides are equal in a triangle then angles will be equal)

So the equation becomes $\angle {\text{WOY}}$+2$\angle {\text{OYW}}$= $180^o$ ……(1)

And we know the sum of angles is one round and equals 360 degrees.

So we can say $\angle {\text{XOZ}}$+$\angle {\text{XOY}}$+$\angle {\text{YOW}}$+$\angle {\text{ZOW}}$=360 …..(2)

We can say $\angle {\text{XOZ}}$=$\angle {\text{YOW}}$ (vertically opposite angles)

And also $\angle {\text{XOY}}$= $\angle {\text{ZOW}}$=$110^o$ (given) (vertically opposite angles)

On putting the values in equation 2 we get the value of equation as:

220+2$\angle {\text{YOW}}$=360

$\angle {\text{YOW}}$=$\dfrac{{140}}{2} = 70$

On putting this value in equation 1 we get the equation as:

70+2$\angle {\text{OYW}}$=180

2$\angle {\text{OYW}}$=110

$\angle {\text{OYW}}$=$\dfrac{{110}}{2} = 55^o$

Hence the value of the angle is 55 degrees i.e. $55^o$.

Note: Whenever you face such types of problems drawing diagrams will help you to visualize and solve the problem and will make it a bit easier. Here in this problem we have used the concepts used in angles in triangles like vertically opposite angles and sum of angles in one round is 360 degrees, sum of all three angles in a triangle is 180. Using these concepts will solve this problem.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India