Lines And Angles- 1 - Class 9 Maths Free MCQ Test with solutions

Let the ∠x be the required angle
Thus, according to the question
    180−x=3(90−x)
=>180−x=270−3x
=>2x=90
=>x=45

Statement (i): A triangle cannot have two right angles because the sum of all angles in a triangle is always 180°. Having two right angles (90° + 90°) would already equal 180°, leaving no room for a third angle.

Statement (ii): A triangle cannot have all angles less than 60°. The sum of all three angles in a triangle must be 180°. If all three angles are less than 60°, their total would be less than 180°, which is not possible.

Statement (iii): A triangle can have two acute angles because an acute angle is less than 90°. For example, in a right triangle, there are two acute angles and one right angle.

(1). If a triangle has all the angles greater than 60∘, the sum of angles of the triangle will be more than 180∘
Only (2). is correct because if all the angles are equal, triangle will be an equilateral triangle and sum of all the angles of the triangle will be 180∘.

If two parallel lines are cut by a transversal, the corresponding angles are congruent. If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

If two angles are complementary, their measures add up to 90 degrees.

• For two angles to sum to 90 degrees, each must be less than 90 degrees.


• An obtuse angle is greater than 90 degrees, so it can't be complementary.


• A right angle is exactly 90 degrees, so it can't pair with another angle to make 90 degrees.


• An acute angle is less than 90 degrees, making it possible to pair with another acute angle to sum to 90 degrees.


 

Therefore, each angle must be an acute angle. Answer: C

The correct option is Option B.

Infinite number of lines can pass through one point.

Let the angle be x
Then the complement angle will be 90^∘ −x

Given x is 14^∘ more than 90^∘ −x
⟹ x = 14^∘ + 90^∘ −x
⟹ 2x = 104^∘
⟹ x = 52^∘
The measure of the angle is 52^∘

Correct option is C
In the above figure straight lines PQ and RS intersect at O.
It is given that θ=3ϕ  .....(1)
∠POR and ∠QOR form linear pair of angles
Also ∠POR=ϕ and ∠QOR=θ 
∠POR+∠QOR=180
ϕ+θ=180
ϕ+3ϕ=180 .....(From 1)
4ϕ=180
ϕ= 180/4 =45
Hence, ∠ϕ=45.

• No common point — Correct. Parallel lines do not intersect at all, so they share no points.

1. Option A: "Neither equal nor supplementary"
   This is incorrect because the angles will either be equal or supplementary.

2. Option B: "Not equal but supplementary"
   This is partially correct but does not include the case when the angles are equal.

3. Option C: "Equal but not supplementary"
   This is also partially correct but does not include the case when the angles are supplementary.

4. Option D: "Either equal or supplementary"
   This is correct as it covers both possibilities.

All are incorrect as it is not given that the lines are parallel. Hence, D option.

Draw a line l and a point P not lying on l.

Now, we can draw a straight line parallel to l which passes through P.

Clearly from the figure, only one line can be drawn which is parallel to l and passes through P.

Option C:

"One of the angles forming a linear pair can be an obtuse angle."

• A linear pair consists of two angles that add up to 180 degrees. One angle can be obtuse (greater than 90 degree) while the other is acute (less than 90 degree).
• This statement is true.

Exterior angle of a triangle = 80°
Let each of the two equal interior opposite angles be x
We use the property of triangles:
An exterior angle of a triangle is equal to the sum of its two interior opposite angles.
Exterior Angle = Sum of two interior angles
x + x = 80°
2x = 80°
x = 80°/2
x = 40°

So, Each Opposite Interior Angles = 40°
​

Let one angle be 2x and the other be 7x.
2x + 7x = 180
9x = 180
x = 180/9 = 20
First angle = 2*20 = 40°
Second angle = 7*20 = 140°

For POQ=straight line →∠ POQ=180^o

2x+30+4x=180

6x+30=180

6x=150

x=25^o.