Question

In the given figure, if $y$ = $3x$ , find the magnitude of $x$.

Explain with complete calculations & justifications.

Points : 15 ☺

Answer 1

Hi!

In the given figure,
Please refer to the figure I have attached
(Sorry it is a little shabby)

First let us name the angles O and P as given in the figure.
Now we know angle CBO= 40'
Therefore angle ABC= 180'-40'=140' (Because angle on a straight line)
Therefore angle PBA= 40'(Vertically Opposite angles)
Now ADC= 180'-140=40' (Because angle opposite angle of cyclic quadrilateral are supplementary)
Now we can see that DA=DC(Chord Property)
Therefore angle PCD=DAO= 90'(Quadilateral= 360')
Now we know PAB is also 90' because it is on a straight line.
Now we can find y by angle sum property
Therefore 180=y+90+40
On solving we get
y=50'
It is given that y=3x
Therefore x=y/3=50/3=16.6'
Therefore angle x= 16.6'

Hope this helps!

Answer 2

see attachment...hope it helps....☺☺☺