The Triangle and its Properties Class 7 MCQ Questions

Answer: (b) 50˚ , 90˚ and 40˚

Explanation: Let the measures of the given angles be:
1st angle = ( 5a )˚

2nd angle = ( 9a )˚

3rd angle = ( 4a )˚

Then, According to angle sum property of triangle

1st angle + 2nd angle + 3rd angle = 180 ˚

5a + 9a + 4a = 180

18a = 180

a = 180/18​​

a = 10

So, 1st angle = ( 5a )˚ = ( 5 x a )˚ = ( 5 x 10 )˚ = 50˚

2nd angle = ( 9a )˚ = ( 9 x a )˚ = ( 9 x 10 )˚ = 90˚

3rd angle = ( 4a )˚ = ( 4 x a )˚ = ( 4 x 10 )˚ = 40˚

Hence, the measures of the angles of the triangle are 50˚ , 90˚ and 40˚

Answer: (d) 40˚

Explanation: Given:
1st angle = 64˚
2nd angle = 76˚
3rd angle = ?

Let, 3rd angle = a

Then, According to angle sum property of triangle
1st angle + 2nd angle + 3rd angle = 180˚
64˚ + 76˚ + a = 180˚
140˚ + a = 180˚
a = 180˚ – 140˚
a = 40˚

Then, 3rd angle = 40˚

Hence, the measure of third angle is 40˚

Answer: (a) 62˚ each

Explanation: Given:
1st angle = 56˚

2nd angle = ?

3rd angle = ?

Let, 2nd angle = a

3rd angle = a

Then, According to angle sum property of the Triangle

1st angle + 2nd angle + 3rd angle = 180˚

56 + a + a = 180˚

56˚ + 2a = 180˚

2a = 180˚ – 56˚

2a = 124˚

a = 62˚

Then, 2nd angle = 62˚

3rd angle = 62˚

Hence, the measure of the each of these equal angle is 62˚

Answer: (b) An Obtuse Triangle

Explanation: Acute Angled triangle – When all the Angles of a Triangle are Acute angles ( less than 90°), we call such a triangle as an Acute angled triangle.

Right Angled Triangle- When one angle of a triangle is 90° and the other two angles are acute ( less than 90°) then we call such a triangle as a Right angled triangle.

Obtuse angled triangle – If one angle of a triangle is obtuse ( greater than 90°) and other two are acute ( less than 90°), we call such a triangle as Obtuse angled triangle.

here,

107 ˚ > 90 ˚

34 ˚ < 90 ˚

39 ˚ < 90 ˚

Since, one angle of a triangle is obtuse ( greater than 90˚ ) and other two are acute angles (less than 90˚)

Hence, the triangle is an Obtuse Triangle

Answer: (b) An Isosceles Triangle

Explanation: Equilateral triangle – When all the three sides of triangle are of equal length, we call it an Equilateral triangle.

Isosceles triangle – When two sides are of triangle are of equal length and one side is different in length from the other, we call it Isosceles triangle.

Scalene triangle – When all the sides of triangle are different in length, we call it Scalene triangle.

Here, sides of triangle are 17 cm , 17 cm , 21 cm

Since, two sides of triangle are of equal length and one is different, so the triangle formed by given side is An Isosceles Triangle

Answer: (a) Yes

Explanation: According to Triangle Inequality Property.

The sum of any two sides of a triangle is greater than the third side.

i.e.,

( a + b – c ) > 0

( a + b ) > c

( b + c – a ) > 0

( b + c ) > a

( c + a – b ) > 0

( c + a ) > b

Clearly we have,

( 22 + 59 – 78 ) > 0

( 22 + 59 ) > 78

81 > 78

Which is True

( 59 + 78 – 22 ) > 0

( 59 + 78 ) > 22

137 > 22

Which is True

( 78 + 22 – 59 ) > 0

( 78 + 22 ) > 59

100 > 59

Which is True

Since, the sum of two sides of a triangle is greater than the third side.

Hence, it is possible to draw a triangle whose sides are 22 cm , 59 cm and 78 cm

Answer: (b) 8 cm

Explanation: According to Pythagoras’ Theorem
In right angled triangle, the square of the hypotenuse equals the sum of the squares of its remaining sides.

c² = a² + b²

Where,

c is hypotenuse

a and b are other two sides

Now we have,

a = 6 cm

b = ?

c = 10 cm

According to Pythagoras’ Theorem

c² = a² + b²

i.e.,

10² cm = 6²cm + b²

100 cm = 36 cm +b²

b²= ( 100 – 36 ) cm

b²= 64 cm

b = 8 cm

Hence, the length of other side is = 8 cm.