I got reference of this Puzzle from Twitter. I uploaded two of its possible and easy solutions. You may line this Puzzle.
So, dare to solve it...
Take a look at figure given below. Give it a try and when you are ready then watch the solution.
Diameter and Circle is drawn. Two random points on either side of diameter are plotted. Angle formed by one end of diameter and two points is 55°. Find angle between one point and diameter as asked in figure.
This is a pretty easy puzzle. But the condition is you have to know some basic concepts.
I used some basic concepts of Geometry to solve this puzzle by two different methods.
Method 1:
First you have to do assume angle DAC as 'p' and BAC as 'q'.
By this You have to calculate p and q.
So that x = p+q
Angle ADC will be 90+q.
For understand this, you have to join B and D then angle ADC will be divided in two parts. One is 90 and other will be lie on arc BC. As we know angle lie on same arc are same since Angle BAC = Angle BDC.
This is the reason for Angle ADC to be 90+q.
Now take a look at this figure:
As we know some of all angles of triangle is 180.
⇒ p+90+q+55 = 180
⇒ p+q = 180-90-55
⇒ x = 35
Method 2:
In this first we join BC.
As we can see its angle inscribed in semicircle.
⇒ Angle ACB = 90
⇒ Angle BCD = 90+55 = 145
We can clearly see that ABCD is a cyclic quadrilateral (Quadrilateral inscribed in a circle).
As we know sum of opposite side of quadrilateral is 180.
⇒ Angle BAD + Angle BCD = 180
⇒ x+145 = 180
⇒ x = 35
