Answer
Verified
424.2k+ views
Hint:Vertical Angles are the angles opposite each other when two lines cross. "Vertical" in this case means they share the same Vertex (corner point).Using this definition we try to find vertical opposite angles from the figure.
Complete step-by-step answer:
The given image is,
Vertical Angles are the angles opposite each other when two lines cross. "Vertical" in this case means they share the same Vertex (corner point).
Here \[AB\] and \[XY\] are two intersecting lines. They meet at \[C\].
Then the vertical angles are \[\angle ACY,{\text{ }}\angle XCB\,\&\, \angle XCA,{\text{ }}\angle BCY\]
The interesting thing here is that, vertical angles are equal.
So,
\[\angle ACY = \angle XCB\]
\[\angle XCA = \angle BCY\]
Thus we get, the pair of vertically opposite angles are \[\angle ACY,{\text{ }}\angle XCB\,\&\, \angle XCA,{\text{ }}\angle BCY\].
Note:When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other. Also, a vertical angle and its adjacent angle are supplementary angles, that is they add up to \[180^\circ \]. For example, if two lines intersect and make an angle, say \[X = 45^\circ \], then its opposite angle is also equal to \[45^\circ \]. And the angle adjacent to angle \[X\] will be equal to \[180^\circ - 45^\circ = 135^\circ \].
When two lines meet at a point in a plane, they are known as intersecting lines. When the lines do not meet at any point in a plane, they are called parallel lines.
Complete step-by-step answer:
The given image is,
Vertical Angles are the angles opposite each other when two lines cross. "Vertical" in this case means they share the same Vertex (corner point).
Here \[AB\] and \[XY\] are two intersecting lines. They meet at \[C\].
Then the vertical angles are \[\angle ACY,{\text{ }}\angle XCB\,\&\, \angle XCA,{\text{ }}\angle BCY\]
The interesting thing here is that, vertical angles are equal.
So,
\[\angle ACY = \angle XCB\]
\[\angle XCA = \angle BCY\]
Thus we get, the pair of vertically opposite angles are \[\angle ACY,{\text{ }}\angle XCB\,\&\, \angle XCA,{\text{ }}\angle BCY\].
Note:When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other. Also, a vertical angle and its adjacent angle are supplementary angles, that is they add up to \[180^\circ \]. For example, if two lines intersect and make an angle, say \[X = 45^\circ \], then its opposite angle is also equal to \[45^\circ \]. And the angle adjacent to angle \[X\] will be equal to \[180^\circ - 45^\circ = 135^\circ \].
When two lines meet at a point in a plane, they are known as intersecting lines. When the lines do not meet at any point in a plane, they are called parallel lines.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Why Are Noble Gases NonReactive class 11 chemistry CBSE
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
At which age domestication of animals started A Neolithic class 11 social science CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Write a letter to the principal requesting him to grant class 10 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE