Vertically Opposite Angles

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Vertically Opposite Angles ( vertical angles ) are the angles opposite each other when two lines cross.

"Vertical" in this case means they share the same Vertex (or corner point).

The measures of vertical angles are equal.

∠ 1 = ∠3

∠ 2 = ∠4

In fact these angles are congruent.

In other word, we can say that two angles formed by two intersecting lines having no common arm are called Vertical Angles.

The measures of vertical angles are equal.

Note : From the above figure, we can say that ∠1 and ∠2 form a linear pair. Also , ∠2 and ∠3; ∠3 and ∠4 ; ∠4 and ∠1.

Examples :

1) Find the value of ‘y’.

Since ∠COD and ∠ EOF are vertical angles.
∴ ∠ COD = ∠ EOF
⇒ ∠COD = 5y0 [∠ EOF = 5y0 (given)]

Now, OA and OB are opposite rays.

∴ ∠AOD + ∠DOC + ∠COB = 1800

⇒ 2y + 5y + 5y = 180

⇒ 12y = 180

⇒ y = 180/12

⇒ y = 15.

1) If the two vertical angles are 5x and 1200 then find the value of x.
2)If two lines intersect each other, then vertical angles are _______.
m∠1 = 350. Find m∠2,m∠3,and m∠4 giving reasons.
4) The two lines l and m intersect each other at O, write the names of vertical angles.
5) Two lines are perpendicular to each other. Write the measure of all four angles formed by these two lines.
Basic Geometry

Lines and Angles
Complementary angles
Supplementary angles
Vertically Opposite Angles
Linear Pair Angles
Adjacent Angles
Parallel Lines
Solved Problems on Intersecting Lines
Solved Problems on Parallel Lines

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