10 Questions MCQ Test Mathematics (Maths) Class 9 - Test: Basic Concepts Of Geometry
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A pair of angles is called linear pair if sum of two adjacent angles is:
Detailed Solution for Test: Basic Concepts Of Geometry - Question 6
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 non-common arms are opposite rays.
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°.
If two lines intersect each other, then the vertically opposite angles are ……….
Detailed Solution for Test: Basic Concepts Of Geometry - Question 8
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
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.
The supplementary angles are in the ratio 4:5 find the angles.
Detailed Solution for Test: Basic Concepts Of Geometry - Question 10
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°
4x + 5x = 180°
4×20° +5×20° = 180°
80°+ 100°= 180°
180° = 180°
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