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Steps: 2 Marks
Actual Reading: 1 Mark
Angle Rotated: 1 Mark
The minute hand whenpoints at 6 cover an angle of 180 degrees.
As per question reading of the minute hand moved is twice the actual reading.
So, it will be pointing at 3.
Now for every five minutes, the minute hand would rotate through 30${}^{\circ }$.
So when the minute hand passes from 12 to 3, total minutes passed =15.
Therefore the actual angle rotated by the minute hand = 3$\times$30 = 90${}^{\circ }$

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Visualisation: 1 Mark
Finding the angle: 1 Mark
Type of Triangle: 1 Mark
The minute hand covers an angle of 30${}^{\circ }$ in every five minutes. The angle covered in moving from4 to 6 is60${}^{\circ }$.
The lengthof the minute hand remains constant. So the two sides of the triangle will be equal.
So the angles will be same for the sides which are equal.
Now, theangle included between the sides whose length are equal is 60${}^{\circ }$.
So the other angles are (180-60)$÷$2 = 60${}^{\circ }$.
Hence all the angles of the triangle are 60${}^{\circ }$.
$\therefore$ The the triangle formed is an equilateral triangle.

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Each Point: 1 Mark
We know that a right angle is equal to 90${}^{\circ }$
a) Any angle less than a right angle is an acute angle.
b)If an angle is greater than 90${}^{\circ }$ and less than 180${}^{\circ }$, then it is called an obtuse angle.
If an angle is greaterthan 180${}^{\circ }$ then it is called a reflex angle.

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Given that
The length of the line segment AB = 5m
The length of the line segment BC = 4m
The length of the line segment AC = 9m
The length of AB+BC = 9m = AC
According to the given conditions, AB + BC = AC. So, B lies in between A and C.

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Solutions: 1 Mark each
a) The length of all sides of the triangle is equal.
So it is an equilateral triangle.
b) In this triangle two sides are=6m
So it is an isosceles triangle.
c) In this triangle one of the angles is 90${}^{\circ }$, so the triangle is a right-angledtriangle.
d) In this triangle, two angles are equal to 70${}^{\circ }$.So it is an isosceles triangle.

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Each option: 1 Mark
(a) A sweet laddu is Spherical in shape.
(b)A road-roller is Cylindrical in shape.
(c)A Matchbox is in the shape of a Cuboid.
(d) A brick is in the shape of a Cuboid.

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Each option: 1 Mark
When the hour hand completes one complete revolution it completes 360 degrees.
a) When the hour hand moves from 3 to 6 it covers 90 degrees. When it moves from 6 to 8 it covers 60 degrees. So, the angle covered when hour hand moves from 3 to 8 is 150 degrees.
Fraction that it has moved = $\frac{150}{360}$ = $\frac{5}{12}$
b) When the hour hand of the clock moves from 3 to 9 it moves through two right angles.
So the angle it covers when it moves from 3 to 9 = 180 ${}^{\circ }$
Fraction that it has moved = $\frac{180}{360}$ = $\frac{1}{2}$

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Steps: 2 Marks
Answer: 1 Mark
The angle covered when the minute hand moves from 3 to 6 is 90 degrees.
Given that:
The sides of the quadrilateral are equal.
So the quadrilateralcan either be a rhombus or a Square.
But the angles included between the sides is 90${}^{\circ }$.
$\therefore$ The quadrilateral is a Square.
Now in asquare, the diagonals intersect each other at 90${}^{\circ }$.
So angle between the diagonals is 90${}^{\circ }$

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Triangle: 2 Marks
Given that:
The sum of two angles of the triangle is 90${}^{\circ }$.
We know that the sum of all the three angles in a triangle is 180${}^{\circ }$.
$\therefore$ The other angle = 180-90 = 90${}^{\circ }$
Now we know that if one of the angles in a triangle is 90${}^{\circ }$, then the triangle is a right-angled triangle.
Hence, the given triangle is a right-angled triangle.

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Each option: 1 Mark
Steps: 1 Mark
A vertex is a point where two edges meet.
An edge is a line segment where two faces meet.
A closed plane formed by line segments is called the face.
a)As we can clearly see in the above figure the various vertices are A,B,C,D,E, F.
b) The various edges are AB, AC, AE, BC, BD, CF, DE, DF.
c) The various faces are DEF, ACFE, BDFC, BAED, BAC.