Q. 24.3( 3 Votes )

The numbers 1, 4,

Answer :

We know that a clock is a circle. And, a circle is made of 360°.


The clock has 12 numbers & each number represents an angle and the separation between them is


Suppose, is the clock reads, 3pm, then the angle subtended at the centre will be equal to 30° × 3 = 90°. (as shown in the figure below)



Now, the figure of the question is given below:



Concept involved:


Theorem (1) : The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.


Now,


COB = 120° (30° × 4)


From theorem (1),


The CAB = 1/2 COB = 60°.


And, ABC = 30° × 3 = 90°.


From theorem (1), ACB = 45°


Now in a triangle, all the angles sum is 180°


, 1 + 4 + 8 = 180°


60° +4 + 45° = 180°


4 = 75°


Hence, all the three angles are 60°, 45° and 75°.


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