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Vertically Opposite Angles

In the given ...

Question

In the given figure, lines AB, CD and EF intersect at O, Find the measure of ∠AOC, ∠COF, ∠DOE and ∠BOF.

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Solution

It is given thatand intersect at a point

Thus and are vertically opposite angles, therefore, these must be equal.

That is,

Similarly,and intersect at a point.

Thusand are vertically opposite angles, therefore, these must be equal.

That is,

Similarly,and intersect at a point.

Thusand are vertically opposite angles, therefore, these must be equal.

That is,

Also,,and form a linear pair. Therefore, their sum must be equal to .

Putting in (I):

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Similar questions

In the given figure, three lines AB, CD and EF intersect at a point O such that $∠ A O E = 35^{\circ}$ and $∠ B O D = 40^{\circ}$ . Find the measure of $∠ A O C, ∠ B O F, ∠ C O F$ and $∠ D O E$ .

∠ A O F = 120^{o}, ∠ B O F = 60^{o}

∠ B O D = 90^{o}

Then find the unknown angles in the figure, where AB,CD and EF are straight lines intersecting at O.

Q. In the given figures, lines

A B

C D

intersect at point

O

∠ A O D + ∠ B O D + ∠ B O C = 300^{\circ}

∠ A O C

Two lines AB and CD intersect at O. If $∠ A O C + ∠ C O B + ∠ B O D = 270^{0}$ , find the measure of $∠ A O C, ∠ C O B, ∠ B O D a n d ∠ D O A$ .

Q. In the given figure, two straight line AB and CD intersect at a point O.
If ∠AOC = 42°, find the measure of each of the angles:

(i) ∠AOD
(ii) ∠BOD
(iii) ∠COB

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