The Triangle and Its Properties Test

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The Triangle and Its Properties Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

One of the angles of a triangle is $$65^o$$. Find the remaining two angles, if their difference is $$25^o$$.

A
$$70^o, 45^o$$

B
$$55^o, 40^o$$

C
$$50^o, 85^o$$

D
$$75^o, 40^o$$

Solution

Let one angle be $$\angle x$$
$$\therefore$$ other angle is $$\angle x+25^o$$
Now,
We know, by angle sum property, the sum of all angles of a triangles is $$ 180^0$$.
$$\implies x+x+25^o+65^o=180^o$$
$$\implies 2x=180^o-90^o$$
$$\implies x=45^o$$
Thus, the angles are $$45^o$$ and $$70^o$$
Question 2
1 / -0

In figure, if lines PQ and RS intersect at point T, such that $$\angle PRT=40^o, \angle RPT=95^o$$ and $$\angle TSQ=75^o$$, find $$\angle SQT$$.

A
$$20^o$$

B
$$ 60^o$$

C
$$30^o$$

D
$$80^o$$

Solution

In $$\triangle PRT$$
$$\angle PTS=\angle PRT+\angle RTP$$ (As exterior angle is equal to sum of interior opposite angles )
$$\Rightarrow \angle PTS={ 95 }^{ \circ }+{ 40 }^{ \circ }={ 135 }^{ \circ }$$

Now in $$\triangle SQT$$
$$\angle STQ=\angle SQT+\angle TSQ$$ (As exterior angle is equal to sum of interior opposite angles )
$$\Rightarrow { 135 }^{ \circ }=\angle SQT+{ 75 }^{ \circ }\\ \Rightarrow \angle SQT={ 135 }^{ \circ }-{ 75 }^{ \circ }={ 60 }^{ \circ }$$
Question 3
1 / -0

The $${\triangle }$$ formed by BC =7.2 cm , AC =6 cm and $${\angle C}$$ = $${120^0}$$ is:

A
An acute angle $${\triangle }$$

B
An obtuse angled $${\triangle }$$

C
A right angled $${\triangle }$$

D
None of these

Solution

Given $$\angle C=120^{\circ}$$
Here one of the angles of the triangle is greater than $$90^{\circ}$$ . So the $$\triangle$$ is obtuse angled triangle.
Therefore option $$B$$ is correct.
Question 4
1 / -0

If two angles in a triangle are $$40^o$$ and $$60^o$$, then the third angle is:

A
$$90^o$$

B
$$80^o$$

C
$$70^o$$

D
$$60^o$$

Solution

Let the third angle be $$x$$
We know, by angle sum property, the sum of all angles of a triangles is $$ 180^0$$.
$${ 40 }^{ \circ }+{ 60 }^{ \circ }+x={ 180 }^{ \circ }\\ { 100 }^{ \circ }+x={ 180 }^{ \circ }\\ \Rightarrow x={ 80 }^{ \circ }$$
Question 5
1 / -0

For any triangle $$ABC$$, the true statement is

A
$${ AC }^{ 2 }={ AB }^{ 2 }+{ BC }^{ 2 }$$

B
$$AC=AB+BC$$

C
$$AC>AB+BC$$

D
$$AC<\,AB+BC$$

Solution

For any $$\triangle ABC$$, the sum of two sides must be greater than the third side.

Hence, $$AB + BC > AC$$.
Question 6
1 / -0

Number of interior angles formed in a triangle are:

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

Number of interior angles formed in a triangle are $$3.$$
Here, $$m\angle A, m\angle B$$ and $$m\angle C$$ stand for measure of angle $$A,B$$ and $$C.$$
Question 7
1 / -0

The given road sign is an equilateral triangle. What is the measure of each angle?

A
$$45^\circ$$

B
$$90^\circ$$

C
$$60^\circ$$

D
$$36^\circ$$

Solution

In an equilateral triangle all the angles are equal . Let each angle be $$x$$
Now by angle sum property
$$x+x+x={ 180 }^{ \circ }\\ \Rightarrow 3x={ 180 }^{ \circ }\\ \Rightarrow x={ 60 }^{ \circ }$$
So option $$C$$ is correct.
Question 8
1 / -0

The sum of all exterior angles of a triangle is

A
$$360^o$$

B
$$180^o$$

C
$$540^o$$

D
none of these

Solution

$$\textbf{Step 1: Naming the angles of the triangle}$$
$$\text{Let the angles of the triangle be }x,\;y,\;\text{and }z$$
$$x+y+z=180^{\circ}$$
$$x+y=\text{Exterior angle A}$$
$$y+z=\text{Exterior angle B}$$
$$x+z=\text{Exterior angle C}$$
$$\textbf{Step 2: Finding sum of exterior angles}$$
$$\text{Sum of exterior angles}=x+y+y+z+x+z$$
$$=2x+2y+2z$$
$$=2(x+y+z)=2\times180=360^{\circ}$$
$$\textbf{Final Answer: The sum of all exterior angles of a triangle is }\mathbf{360^{\circ}}.$$
Question 9
1 / -0

In the given figure, XYZ is a/an_________triangle.

A
isosceles

B
equilateral

C
scalene

D
none of these

Solution

In the given $$\triangle XYZ,$$
$$XY = XZ = 8$$ cm
Since two sides are equal of the given triangle.
$$\therefore \triangle XYZ $$ is an isosceles triangle.
Option A is correct.
Question 10
1 / -0

A triangle with the sides measuring $$4$$ cm, $$5$$ cm and $$5$$ cm is called

A
an equilateral triangle

B
an isosceles triangle

C
a scalene triangle

D
none of the above

Solution

Given, the sides of the triangle are $$4$$ cm, $$5$$ cm and $$5$$ cm
A triangle having two equal sides is called an isosceles triangle.
Here, two sides of the triangle are $$5$$ cm and $$5$$ cm. So, it is an isosceles triangle.
So, option B is correct.

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Re-Attempt Weekly Quiz Competition

The Triangle and Its Properties Test - 6

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The Triangle and Its Properties Test - 6

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SHARING IS CARING

Question 1

$$70^o, 45^o$$

$$55^o, 40^o$$

$$50^o, 85^o$$

$$75^o, 40^o$$

Solution

Question 2

$$20^o$$

$$ 60^o$$

$$30^o$$

$$80^o$$

Solution

Question 3

An acute angle $${\triangle }$$

An obtuse angled $${\triangle }$$

A right angled $${\triangle }$$

None of these

Solution

Question 4

$$90^o$$

$$80^o$$

$$70^o$$

$$60^o$$

Solution

Question 5

$${ AC }^{ 2 }={ AB }^{ 2 }+{ BC }^{ 2 }$$

$$AC=AB+BC$$

$$AC>AB+BC$$

$$AC<\,AB+BC$$

Solution

Question 6

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 7

$$45^\circ$$

$$90^\circ$$

$$60^\circ$$

$$36^\circ$$

Solution

Question 8

$$360^o$$

$$180^o$$

$$540^o$$

none of these

Solution

Question 9

isosceles

equilateral

scalene

none of these

Solution

Question 10

an equilateral triangle

an isosceles triangle

a scalene triangle

none of the above

Solution

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