Question 12 Marks
Define the following terms:
Angle.
Angle.
Answer
View full question & answer→rays OA and OB, with a common end-point O, form an angle AOB that is represented as $\angle\text{AOB}.$
Questions
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19 questions · timed · auto-graded
Question 22 Marks
Define the following terms:
Supplementary angles.
Supplementary angles.
Answer
View full question & answer→Two angles are said to be supplementary if the sum of their measures is 180º.
Question 32 Marks
For what value of x will the lines l and m be parallel to each other?
Answer
View full question & answer→Lines l and m will be parallel if 3x - 20 = 2x + 10
[Since, if corresponding angles are equal, lines are parallel]
⇒ 3x - 2x = 10 + 20
⇒ x = 30
[Since, if corresponding angles are equal, lines are parallel]
⇒ 3x - 2x = 10 + 20
⇒ x = 30
Question 42 Marks
Define the following terms:
Reflex angle.
Reflex angle.
Answer
View full question & answer→An angle greater than 180º but less than 360º is called a reflex angle.
Question 52 Marks
In the figure given below, state which lines are parallel and why?
Answer
View full question & answer→In the given figure,
$\angle\text{BAC}=\angle\text{ACD}=110^\circ$
But, these are alternate angles when transversal AC cuts AB and CD.
Hence, AB || CD.
$\angle\text{BAC}=\angle\text{ACD}=110^\circ$
But, these are alternate angles when transversal AC cuts AB and CD.
Hence, AB || CD.
Question 62 Marks
Find the angle which is four times its complement.
Answer
View full question & answer→Let the measure of the required angle be x.
Then, measure of its complement = (90º - x).
Therefore,
x = (90º - x)4
⇒ x = 360º - 4x
⇒ 5x = 360º
⇒ x = 72º
Hence, the measure of the required angle is 72º.
Then, measure of its complement = (90º - x).
Therefore,
x = (90º - x)4
⇒ x = 360º - 4x
⇒ 5x = 360º
⇒ x = 72º
Hence, the measure of the required angle is 72º.
Question 72 Marks
Find theangle which is five times its supplement.
Answer
View full question & answer→Let the measure of the required angle be x.
Then, measure of its supplement = (180º - x).
Therefore,
x = (180º - x)5
⇒ x = 900º - 5x
⇒ 6x = 900º
x = 150º
Hence, the measure of the required angle is 150º.
Then, measure of its supplement = (180º - x).
Therefore,
x = (180º - x)5
⇒ x = 900º - 5x
⇒ 6x = 900º
x = 150º
Hence, the measure of the required angle is 150º.
Question 82 Marks
Define the following terms:
Obtuse angle.
Obtuse angle.
Answer
View full question & answer→An angle greater than 90º but less than 180º is called an obtuse angle.
Question 92 Marks
Two lines AB and CD intersect at O. If $\angle\text{AOC}=50^\circ,$ find $\angle\text{AOD},\angle\text{BOD}$ and $\angle\text{BOC}.$
Answer
View full question & answer→We know that if two lines intersect then the vertically-opposite angle are equal.
Therefore,
$\angle\text{AOC}=\angle\text{BOD}=50^\circ$
Let $\angle\text{AOD}=\angle\text{BOC}=\text{x}^\circ$
Also, we know that the sum of all angles around a point is 360°.
Therefore,
$\angle\text{AOC}+\angle\text{AOD}+\angle\text{BOD}+\angle\text{BOC}=360^\circ$
⇒ 50 + x + 50 + x = 360º
⇒ 2x = 260º
⇒ x = 130º
Hence, $\angle\text{AOD}=\angle\text{BOC}=130^\circ$
Therefore, $\angle\text{AOD}=130^\circ,\angle\text{BOD}=50^\circ$ and $\angle\text{BOC}=130^\circ.$
Therefore,
$\angle\text{AOC}=\angle\text{BOD}=50^\circ$
Let $\angle\text{AOD}=\angle\text{BOC}=\text{x}^\circ$
Also, we know that the sum of all angles around a point is 360°.
Therefore,
$\angle\text{AOC}+\angle\text{AOD}+\angle\text{BOD}+\angle\text{BOC}=360^\circ$
⇒ 50 + x + 50 + x = 360º
⇒ 2x = 260º
⇒ x = 130º
Hence, $\angle\text{AOD}=\angle\text{BOC}=130^\circ$
Therefore, $\angle\text{AOD}=130^\circ,\angle\text{BOD}=50^\circ$ and $\angle\text{BOC}=130^\circ.$
Question 102 Marks
Find the measure of an angle which is:
Equal to its supplement.
Equal to its supplement.
Answer
View full question & answer→Let the measure of the rquired angle be xº.
Then, in case of supplementary angle:
x + x = 180º
⇒ 2x = 180º
⇒ x = 90º
Hence, measure of the angle that is equal to its supplement is 90º.
Then, in case of supplementary angle:
x + x = 180º
⇒ 2x = 180º
⇒ x = 90º
Hence, measure of the angle that is equal to its supplement is 90º.
Question 112 Marks
Find the measure of an angle which is:
Equal to its complement.
Equal to its complement.
Answer
View full question & answer→Let the measure of the required angle be xº.
Then, in case of complementary angle:
x + x = 90º
⇒ 2x = 90º
⇒ x = 45º
Hence, measure of the angle that is equal to its complement is 45º.
Then, in case of complementary angle:
x + x = 90º
⇒ 2x = 90º
⇒ x = 45º
Hence, measure of the angle that is equal to its complement is 45º.
Question 122 Marks
In the adjoining figure, what value of x will make AOB a straight line?
Answer
View full question & answer→AOB will be a straight line if
3x + 20 + 4x - 36 = 180º
⇒ 7x = 196º
⇒ x = 28º
Hence, x = 28 will make AOB a striaght line.
3x + 20 + 4x - 36 = 180º
⇒ 7x = 196º
⇒ x = 28º
Hence, x = 28 will make AOB a striaght line.
Question 132 Marks
For what value of x will the lines l and m be parallel to each other?
Answer
View full question & answer→⇔ 3x + 5 + 4x = 180 [Consecutive Interior Angle]
⇔ 7x = 175
⇔ x = 25
⇔ 7x = 175
⇔ x = 25
Question 142 Marks
Define the following terms:
Complementary angles.
Complementary angles.
Answer
View full question & answer→Two angles are said to be complementry if the sum of their measures is 90º.
Question 152 Marks
Find the measure of an angle which is 36º more than its complement.
Answer
View full question & answer→Let the measure of the required angle be xº.
then, measure of its complement = (90 - x)º.
Therefore,
x - (90º - x) = 36º
⇒ 2x = 126º
⇒ x = 63º
Hence, the measure of the required angle is 63º.
then, measure of its complement = (90 - x)º.
Therefore,
x - (90º - x) = 36º
⇒ 2x = 126º
⇒ x = 63º
Hence, the measure of the required angle is 63º.
Question 162 Marks
In the adjoining figure, AOB is a straight line. Find the value of x.
Answer
View full question & answer→We know that the sum of angles in a linear pair is 180º.
Therefore,
$\angle\text{AOC}+\angle\text{BOC}=180^\circ$
⇒ 62º + xº = 180º
⇒ xº = (180º - 62º)
⇒ x = 118º
Hence, the value of x is 118º.
Therefore,
$\angle\text{AOC}+\angle\text{BOC}=180^\circ$
⇒ 62º + xº = 180º
⇒ xº = (180º - 62º)
⇒ x = 118º
Hence, the value of x is 118º.
Question 172 Marks
Two complementary angles are in the ratio 4 : 5. Find the angles.
Answer
View full question & answer→Let the angles be 4x and 5x, respectively.
Then,
4x + 5x = 90
⇒ 9x = 90
⇒ x = 10º
Hence, the two angles are 4x = 4 × 10º = 40º and 5x = 5 × 10º = 50º.
Then,
4x + 5x = 90
⇒ 9x = 90
⇒ x = 10º
Hence, the two angles are 4x = 4 × 10º = 40º and 5x = 5 × 10º = 50º.
Question 182 Marks
Two adjacent angles on a straight line are in the ratio 5 : 4. Find the measure of each of these angles.
Answer
View full question & answer→Let the two adjacent angles be 5x and 4x, respectively.
Then,
5x + 4x = 180º
⇒ 9x = 180º
⇒ x = 20º
Hence, the two angles are 5 × 20º = 100º and 4 × 20º = 80º.
Then,
5x + 4x = 180º
⇒ 9x = 180º
⇒ x = 20º
Hence, the two angles are 5 × 20º = 100º and 4 × 20º = 80º.
Question 192 Marks
Define the following terms:
Interior of an angle.
Interior of an angle.
Answer
View full question & answer→The interior of an angle is the set of all points in its plane, which lie on the same side of OA as B and also on the same side of as A.
