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14.  In the adjoining figure, name the following pairs of angles.

(i) Obtuse vertically opposite angles
(iii) Equal supplementary angles
(iv) Unequal supplementary angles
(v) Adjacent angles that do not form a linear pair

(i)   are the vertically obtuse angles.  (ii)   are the complementary angles. (iii)   are the equal supplementary angles. (iv)   are the unequal pair of supplementary angle. (v)  ,   and   are adjacent angles but are not supplementary angles.

13.  Fill in the blanks:

(i) If two angles are complementary, then the sum of their measures is _______.

(ii) If two angles are supplementary, then the sum of their measures is ______.

(iii) Two angles forming a linear pair are _______________.

(iv) If two adjacent angles are supplementary, they form a ___________.

(v) If two lines intersect at a point, then the vertically opposite angles are always _____________.

(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are  __________.

(i)      (ii)     (iii)   Supplementary angles (iv)   Straight line (v)     equal (vi)   obtuse angles (as they form a line).

12.(ii)  Find the values of the angles x, y, and z in each of the following:

From the figure we can observe that :  (i)                       (Vertically opposite angle) (ii)             (Linear pair/straight line) (iii)          (Vertically opposite angle).

12.(i) Find the values of the angles x, y, and z in each of the following:

From the figure : (i)             (Vertically opposite angle) (ii)      (Linear pair) (iii)                     (Vertically opposite angle)

10.(ii)  Indicate which pairs of angles are:

(ii) Linear pairs

The sum of angles in linear pair is . Thus the linear pairs are :    (a)     (b)

10.(i)   Indicate which pairs of angles are:

(i) Vertically opposite angles.

The vertically opposite pairs are :               (a)    and                 (b)    and

11. In the following figure, is $\angle 1$ adjacent to $\angle 2$? Give reasons.

No,   and    are not adjacent angles as their vertex is not same/common. For being adjacent angles the pair must have a common vertex and have a common arm.

(i) Is $\angle 1$ adjacent to $\angle 2$ ?
(ii) Is $\angle AOC$ adjacent to $\angle AOE$ ?
(iii) Do $\angle COE$ and $\angle EOD$ form a linear pair?
(iv) Are $\angle BOD$ and $\angle DOA$ supplementary?
(v) Is $\angle 1$ vertically opposite to $\angle 4$ ?
(vi) What is the vertically opposite angle of $\angle 5$ ?

(i) Yes,  adjacent to  as these have the same vertex and have one common arm. (ii)  No,   is not adjacent to . This is because  contains . (iii) Yes the given angles form a linear pair as they are pair of supplementary angles. (iv) Since BOA is a straight line thus the given angles are supplementary. (v) Yes,  and  are vertically opposite angles as they are the angles formed by two intersecting...

8. An angle is greater than $45^{o}$. Is its complementary angle greater than $45^{o}$ or equal to $45^{o}$ or less than $45^{o}$?

We know that the sum of two complementary angles is  . Thus if one of the angles is greater than  then the other angle needs to be less than .

7.  Can two angles be supplementary if both of them are:

(i) acute ?   (ii) obtuse ?   (iii) right ?

We know that the sum of supplementary angles is . (i) The maximum value of the sum of two acute angles is less than . Thus two acute angles can never be supplementary. (ii) The minimum value of the sum of two obtuse angles is more than . Thus two obtuse angles can never be supplementary. (iii) Sum of two right angles is . Hence two right angles are supplementary.

6.  In the given figure, $\angle 1$ and $\angle 2$ are supplementary angles. If $\angle 1$ is decreased, what changes should take place in $\angle 2$ so that both the angles still remain supplementary.

Since it is given that  and  are supplementary angles, i.e. the sum of both angles is . Thus if  is decreased then to maintain the sum  needs to be increased.

5.  Find the angle which is equal to its supplement.

Let the required angle be . Then according to the question :                                                      or                                                            or                                                               Hence the angle is .

4. Find the angle which is equal to its complement.

Let the required angle be . Then according to question, we have :                                                       or                                                             or

3. Identify which of the following pairs of angles are complementary and which are supplementary.

$(i) 65^{o},115^{o}$        $(ii) 63^{o}, 27^{o}$     $(iii) 112^{o}, 68^{o}$

$(iv) 130^{o}, 50^{o}$      $(v) 45^{o}, 45^{o}$      $(vi) 80^{o}, 10^{o}$

We know that the sum of supplementary angles is   and the sum of complementary angle is . (i) Sum of the angles is :    . Hence these are supplementary angles. (ii) Sum of the angles is :    . Hence these are complementary angles. (iii) Sum of the angles is :    . Hence these are supplementary angles. (iv) Sum of the angles is :    . Hence these are supplementary angles. (v) Sum of the angles...

2.(iii)  Find the supplement of each of the following angles:

We know that the sum of angles of supplementary pair is . Thus the supplement of the given angle is :

2.(ii) Find the supplement of each of the following angles:

We know that the sum of angles of supplementary pair is . Thus the supplement of the given angle is :

2.(i)   Find the supplement of each of the following angles:

We know that sum of supplement angles is   The supplement of the given angle is :

1.(iii)  Find the complement of each of the following angles:

The sum of complement angles is . Thus the complement of the angle is given by :

1.(ii)  Find the complement of each of the following angles:

The sum of the complementary angle is . Thus the complementary angle to the given angle is :

1.(i)  Find the complement of each of the following angles:

The sum of complementary angle is . Thus the complementary angle to the given angle is :
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