Q: 1. Find the complement of each of the following angles: (i) $20^\circ$ (ii) $63^\circ$ (iii) $57^\circ$. 2. Find the supplement of each of the following angles: (i) $105^\circ$ (ii) $87^\circ$ (iii) $154^\circ$. 3. Identify which of the following pairs of angles are complementary and which are supplementary. (i) $65^\circ,115^\circ$ (ii) $63^\circ,27^\circ$ (iii) $112^\circ,68^\circ$ (iv) $130^\circ,50^\circ$ (v) $45^\circ,45^\circ$ (vi) $80^\circ,10^\circ$. 4. Find the angle which is equal to its complement. 5. Find the angle which is equal to its supplement. 6. In the given figure, $\angle1$ and $\angle2$ are supplementary angles. The figure shows two adjacent angles $\angle1$ and $\angle2$ forming a straight line. If $\angle1$ is decreased, what changes should take place in $\angle2$ so that both the angles still remain supplementary. 7. Can two angles be supplementary if both of them are: (i) acute? (ii) obtuse? (iii) right? 8. An angle is greater than $45^\circ$. Is its complementary angle greater than $45^\circ$ or equal to $45^\circ$ or less than $45^\circ$? 9. 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) If two adjacent angles are supplementary, they form a ___________. 10. In the adjoining figure, name the following pairs of angles. The figure has point O with rays OB and OD forming a straight horizontal line, rays OA and OC forming another straight line through O, and ray OE vertical upward. (i) Obtuse vertically opposite angles (ii) Adjacent complementary angles (iii) Equal supplementary angles (iv) Unequal supplementary angles (v) Adjacent angles that do not form a linear pair.

1. (i) $70^\circ$ (ii) $27^\circ$ (iii) $33^\circ$. 2. (i) $75^\circ$ (ii) $93^\circ$ (iii) $26^\circ$. 3. (i) supplementary (ii) complementary (iii) supplementary (iv) supplementary (v) complementary (vi) complementary. 4. $45^\circ$. 5. $90^\circ$. 6. $\angle2$ should be increased by the same measure by which $\angle1$ is decreased, so that their sum remains $180^\circ$. 7. (i) No (ii) No (iii) Yes. 8. Its complementary angle is less than $45^\circ$. 9. (i) $90^\circ$ (ii) $180^\circ$ (iii) linear pair. 10. (i) $\angle AOD$ and $\angle BOC$ (ii) $\angle EOA$ and $\angle AOB$ (iii) $\angle EOB$ and $\angle EOD$ (iv) $\angle EOA$ and $\angle EOC$ (v) $\angle AOB$ and $\angle AOE$; $\angle AOE$ and $\angle EOD$; $\angle EOD$ and $\angle COD$.

Question 1

1. Find the complement of each of the following angles: (i) $20^\circ$ (ii) $63^\circ$ (iii) $57^\circ$. 2. Find the supplement of each of the following angles: (i) $105^\circ$ (ii) $87^\circ$ (iii) $154^\circ$. 3. Identify which of the following pairs of angles are complementary and which are supplementary. (i) $65^\circ,115^\circ$ (ii) $63^\circ,27^\circ$ (iii) $112^\circ,68^\circ$ (iv) $130^\circ,50^\circ$ (v) $45^\circ,45^\circ$ (vi) $80^\circ,10^\circ$. 4. Find the angle which is equal to its complement. 5. Find the angle which is equal to its supplement. 6. In the given figure, $\angle1$ and $\angle2$ are supplementary angles. The figure shows two adjacent angles $\angle1$ and $\angle2$ forming a straight line. If $\angle1$ is decreased, what changes should take place in $\angle2$ so that both the angles still remain supplementary. 7. Can two angles be supplementary if both of them are: (i) acute? (ii) obtuse? (iii) right? 8. An angle is greater than $45^\circ$. Is its complementary angle greater than $45^\circ$ or equal to $45^\circ$ or less than $45^\circ$? 9. 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) If two adjacent angles are supplementary, they form a ___________. 10. In the adjoining figure, name the following pairs of angles. The figure has point O with rays OB and OD forming a straight horizontal line, rays OA and OC forming another straight line through O, and ray OE vertical upward. (i) Obtuse vertically opposite angles (ii) Adjacent complementary angles (iii) Equal supplementary angles (iv) Unequal supplementary angles (v) Adjacent angles that do not form a linear pair.

Accepted Answer

1. (i)

70^\circ

(ii)

27^\circ

(iii)

33^\circ

.
2. (i)

75^\circ

(ii)

93^\circ

(iii)

26^\circ

.
3. (i) supplementary (ii) complementary (iii) supplementary (iv) supplementary (v) complementary (vi) complementary.
4.

45^\circ

.
5.

90^\circ

.
6.

\angle2

should be increased by the same measure by which

\angle1

is decreased, so that their sum remains

180^\circ

.
7. (i) No (ii) No (iii) Yes.
8. Its complementary angle is less than

45^\circ

.
9. (i)

90^\circ

(ii)

180^\circ

(iii) linear pair.
10. (i)

\angle AOD

and

\angle BOC

(ii)

\angle EOA

and

\angle AOB

(iii)

\angle EOB

and

\angle EOD

(iv)

\angle EOA

and

\angle EOC

(v)

\angle AOB

and

\angle AOE

;

\angle AOE

and

\angle EOD

;

\angle EOD

and

\angle COD

.

Question 2

1. State the property that is used in each of the following statements? In the figure, parallel lines $a$ and $b$ are cut by a transversal and the angles are numbered 1, 2, 3, 4 at the upper intersection and 5, 6, 7, 8 at the lower intersection. (i) If $a\parallel b$, then $\angle1=\angle5$. (ii) If $\angle4=\angle6$, then $a\parallel b$. (iii) If $\angle4+\angle5=180^\circ$, then $a\parallel b$. 2. In the adjoining figure, identify (i) the pairs of corresponding angles. (ii) the pairs of alternate interior angles. (iii) the pairs of interior angles on the same side of the transversal. (iv) the vertically opposite angles. The figure has two lines $a$ and $b$ cut by transversal $c$; at the upper intersection angles 4, 1, 2, 3 go around the point, and at the lower intersection angles 8, 5, 6, 7 go around the point. 3. In the adjoining figure, $p\parallel q$. Find the unknown angles. The figure has parallel vertical lines $p$ and $q$ cut by a slant transversal; at line $p$, the lower-left angle is $125^\circ$, the upper-right angle is $e$ and the lower-right angle is $f$; at line $q$, the upper-left angle is $a$, upper-right is $b$, lower-right is $c$ and lower-left is $d$. 4. Find the value of $x$ in each of the following figures if $l\parallel m$. (i) Lines $l$ and $m$ are parallel and cut by transversal $t$; the angle above $l$ on the left of $t$ is $110^\circ$, and $x$ is above $m$ on the left of $t$. (ii) Lines $a$ and $b$ are parallel, and parallel transversals $l$ and $m$ cut them; at $l$, the angle above $a$ on the left is $100^\circ$ and the angle above $b$ on the right is $80^\circ$; at $m$, $x$ is above $a$ on the left. 5. In the given figure, the arms of two angles are parallel. If $\angle ABC=70^\circ$, then find (i) $\angle DGC$ (ii) $\angle DEF$. The figure shows $BA\parallel GD$, $BC\parallel EF$, $B,G,C$ on one straight line, and $D,G,E$ on one slant line. 6. In the given figures below, decide whether $l$ is parallel to $m$. (i) A transversal $n$ cuts $l$ and $m$ with interior angles $126^\circ$ and $44^\circ$ on the same side. (ii) A transversal $n$ cuts lines $l$ and $m$ with a $75^\circ$ angle at each intersection. (iii) A transversal $n$ cuts $l$ and $m$ with angles $57^\circ$ and $123^\circ$ on the same side. (iv) A transversal $n$ cuts $l$ and $m$ with angles $98^\circ$ and $72^\circ$.

Accepted Answer

1. (i) Corresponding angles property (ii) Converse of alternate interior angles property (iii) Converse of interior angles on the same side of the transversal being supplementary.
2. (i) Corresponding angles:

\angle1,\angle5

;

\angle2,\angle6

;

\angle3,\angle7

;

\angle4,\angle8

(ii) Alternate interior angles:

\angle2,\angle8

;

\angle3,\angle5

(iii) Interior angles on the same side of the transversal:

\angle2,\angle5

;

\angle3,\angle8

(iv) Vertically opposite angles:

\angle1,\angle3

;

\angle2,\angle4

;

\angle5,\angle7

;

\angle6,\angle8

.
3.

a=55^\circ

,

b=125^\circ

,

c=55^\circ

,

d=125^\circ

,

e=55^\circ

,

f=55^\circ

.
4. (i)

x=70^\circ

(ii)

x=100^\circ

.
5. (i)

\angle DGC=70^\circ

(ii)

\angle DEF=70^\circ

.
6. (i)

$l$

is not parallel to

$m$

(ii)

$l$

is not parallel to

$m$

(iii)

$l$

is parallel to

$m$

(iv)

$l$

is not parallel to

$m$

.