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Question

If the given figure, ∠AOF and ∠FOG form a linear pair.
∠EOB = ∠FOC = 90° and ∠DOC = ∠FOG = ∠AOB = 30°


(i) Find the measure of ∠FOE, ∠COB and ∠DOE.
(ii) Name all the right angles.
(iii) Name three pairs of adjacent complementary angles.
(iv) Name three pairs of adjacent supplementary angles.
(v) Name three pairs of adjacent angles.

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Solution

The given figure is as follows:

(i)

It is given that,,and form a linear pair .

Therefore, their sum must be equal to .

That is ,

It is given that :

,

and

in equation above, we get:

It is given that:

From the above figure:

Similarly, we have:

From the above figure:

(ii)

We have:

From the figure above and the measurements of the calculated angles we get two right angles as and.

Two right angles are already given asand.

(iii)

We have to find the three pair of adjacent complementary angles.

We know that is a right angle.

Therefore,

and are complementary angles.

Similarly, is a right angle.

Therefore,

and are complementary angles.

Similarly, is a right angle.

Therefore,

and are complementary angles.

(iv)

We have to find the three pair of adjacent supplementary angles.

Since,is a straight line.

Therefore, following are the three linear pair, which are supplementary:

and ;

and and

and

(v)

We have to find three pair of adjacent angles, which are as follows:

and

and

and


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