Free Lines and Angles 03 Practice Test - 9th Grade
Question 1
The angles of a triangle are in the ratio 5:3:7. The triangle is
An isosceles triangle
An acute angled triangle
An obtuse angled triangle
A right triangle
SOLUTION
Solution : B
The sum of all the three angles of a triangle = 180∘
Since the angles are in the ratio 5:3:7, let x be a factor such that,
5x+3x+7x =180∘
⇒ 15x =180∘
⇒ x =12∘
Hence the three angles of the triangle are:
⇒ 5x =5×12∘ =60∘
⇒ 3x =3×12∘ =36∘
⇒ 7x =7×12∘ =84∘
Since all the angles in the triangle are less than 90∘, the triangle is an acute angled triangle.
Question 2
The sum of the two angles in a triangle is 95∘ and their difference is 25∘. Then which of the following are true?
One of the angles is 35∘.
One of the angles is 50∘
One of the angles is 60∘
One of the angles is 85∘
SOLUTION
Solution : A, C, and D
Let the two angles be x and y.
So, x+y=95∘
⇒x=95∘−y ⋅⋅⋅ (i)and, x−y=25∘ ⋅⋅⋅ (ii)
Substitute (i) in (ii),
⇒95∘−y−y=25∘⇒95∘−2y=25∘
⇒y=95∘−25∘2
⇒y=35∘So, x=95∘−35∘
⇒ x=60∘
Third angle is 180∘−95∘=85∘
So, the angles are 35∘, 60∘ and 85∘.
Question 3
An exterior angle of a triangle is 105o and its two interior opposite angles are equal. Each of these equal interior angles are
37.5∘
52.5∘
72.5∘
75∘
SOLUTION
Solution : B
From the properties of triangles:
Exterior angle = Sum of interior opposite angles
Now let us take each interior opposite angle as x ( as both interior opposite angles are equal)
⇒ x + x = 105∘
⇒ 2x = 105∘
⇒ x = 52.5∘
So the value of each of the opposite interior angle = 52.5∘
Question 4
In triangle ABC, if BC=AC and ∠B=40∘. Then ∠C is equal to
SOLUTION
Solution :In a triangle, if two sides are equal then it is an isosceles triangle. The angles opposite to the two equal sides are also equal.
Therefore, ∠A=∠B
Since sum of all the angles in a triangle =180∘
⇒ ∠A+∠B+∠C=180∘
⇒ 2×40∘+∠C=180∘ (∠A=∠B)
⇒ ∠C=180∘−2×40∘
⇒ ∠C=100∘
Question 5
From the figure given below, find out the measure of ∠COB and ∠AOC respectively.
24∘ and 126∘
42∘ and 156∘
24∘ and 156∘
42∘ and 126∘
SOLUTION
Solution : C
Since AB is a straight line, ∠AOB=180∘
Therefore, ∠AOC+∠COB=180∘
⇒3x+30∘+2x−60∘=180∘
⇒5x−30∘=180∘
⇒5x=210∘
⇒x=42∘
Therefore,
∠COB=2x−60∘=84∘−60∘=24∘
∠AOC=3x+30∘=126∘+30∘=156∘
Question 6
If two angles are complementary to each other, then each angle is an acute angle.
True
False
SOLUTION
Solution : A
The sum of two complementary angles is 90∘. Hence, each angle will be less than 90∘
Question 7
Which of the following statements is not correct?
SOLUTION
Solution : C
a)An acute angle measures between 0∘ and 90∘, whereas a right angle is exactly equal to 90∘.
b)An angle greater than 90∘ but less than 180∘ is called an obtuse angle.
c)An angle which is greater than 180∘ but less than 360∘ is called a reflex angle.
d)If the sum of two angles is 90∘, then they are called complementary angles and if the sum is 180∘, then they are called supplementary angles.
Question 8
In the adjoining figure AB || CD, ∠1 : ∠2 = 3 : 2. Then ∠6 is _____
72∘
36∘
100∘
144∘
SOLUTION
Solution : A
Let ∠1 = 3x and ∠2 = 2x
Sum of angles on a straight line is 180∘.
So, 3x + 2x = 180∘
⇒ 5x = 180∘
⇒ x = 36∘
⇒∠6 = ∠2 [∵∠6 and ∠2 are corresponding angles]
⇒ ∠6 = 2x = 2 × 36 = 72∘Hence, ∠6 = 72∘
Question 9
The following diagram shows parallel lines cut by a transversal. Find x.
SOLUTION
Solution : A
In the above figure, since the two lines are parallel and cut by a transversal, using the property of corresponding angles:
⇒ 2x - 60∘ = x
⇒ x - 60∘ = 0
⇒ x = 60∘
Question 10
In the figure, the bisector of B and C meet at O. Then ∠ BOC is
90∘+12∠A
90∘+12∠B
90∘+12∠C
90∘−12∠A
SOLUTION
Solution : A
From the given figure,
∠BOC = 180∘−(∠2 + ∠4)= 180∘ - (∠B2 + ∠C2 )
= 180∘ - (180∘−∠A2)
[∵ 180∘ - ∠ A = ∠ B + ∠ C]= 180∘ - 90∘ + ∠A2
= 90∘ + ∠A2