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The measure of an angle which is a supplement of itself is :
Let the angle = x
Supplement of angle= 180x
ATQ
180x = x
180 = 2x
x = 90°
And its supplement will be 18090=90°
Two lines in a plane are said to be parallel if they do not intersect, when extended infinitely in both the direction.
Also, the distance between the two lines is the same throughout.
The angle whose complement is onethird of its supplement will be
Let the angle be x
complement of x is (90 − x)°
supplement of x is (180 − x)°
Given (90 − x)° = (1/3) × (180 − x)°
⇒ 270° − 3x = 180°− x
⇒ 270° − 180° = 3x − x
⇒ 2x = 90°
∴ x = 45°
Given four points such that no three of them are collinear, then the number of lines that can be drawn through them are:
Given, four points such that no three of them are collunear.
we kow that line can be formed using two points. therfore,
A pair of angles is called linear pair if sum of two adjacent angles is:
Two angles form a linear pair if they have;
A common arm
A common vertex
Their interiors do not overlap
The sum of two angles is 180°.
Therefore, linear pair of angles are adjacent angles whose noncommon arms are opposite rays.
Note:
All adjacent angles do not form a linear pair.
From the above figure we can observe; OX and OY are two opposite rays and ∠XOZ and ∠YOZ are the adjacent angles. Therefore, ∠XOZ and ∠YOZ form a linear pair.
If you measure ∠XOZ and ∠YOZ with the help of the protractor, you will find the sum of their measures equal to 180°.
Thus, the sum of the angles in a linear pair is 180°.
Find the measure of the angle which is complement of itself.
Let the angle be x. Its complement will be 90  x. Therefore,
x = 90  x
=> 2x = 90
=> x = 45 degree
The answer is 45 degree.
If two lines intersect each other, then the vertically opposite angles are ……….
If two straight lines intersect each other at any point then the angle which are vetically opposite are equal.
Given two lines AB and CD intersect each other at the point O.
To prove: ∠1 = ∠3 and ∠2 = ∠4
Proof:
From the figure, ∠1 + ∠2 = 180° [Linear pair] → (1)
∠2 + ∠3 = 180° [Linear pair] → (2)
From (1) and (2), we get
∠1 + ∠2 = ∠2 + ∠3
∴ ∠1 = ∠3
Similarly, we can prove ∠2 = ∠4 also.
If two angles are said to be supplementary angles and one of the angle is of 122° then the other angle is of
Let the angle be = x _{}the supplement = 180^{o} – x
According to the question,
x = 2(180^{o} – x)
3x = 360^{o}
x = 120^{o}
The supplementary angles are in the ratio 4:5 find the angles.
Let the angles be x
As they are in ratio of 4:5, so we can write it in the form of 4x ,5x
We know supplementary angle =180°
so,According to the question
4x+5x = 180°
9x = 180°
x = 180° ÷ 9
x = 20°
so, 1 st angle = 4x = 4×20° = 80°
2 nd angle = 5x = 5×20° = 100°
PROOF
4x + 5x = 180°
4×20° +5×20° = 180°
80°+ 100°= 180°
180° = 180°
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