Question

ncert class 9 maths exercise 10.5 Q. 3

Answer 1

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Answer 2

Given:PQR angle= 100*
TO FIND: Angle OPR
Now,
angle POR= 200*..(angle subted by an arc at
the centre is double the
angle subtend by a
chord at remaining part.)
Now,
Angle POR + Angle ROP = 360*
200 + Angle ROP = 360
Angle ROP= 360-200
Angle ROP= 160*

Now,in triangle POR
Angle OPR + angle PRO + angle ROP= 180*
( angle sum property)
Now ,
Angle OPR = Angle PRO
And let these angles be x
So,
x+x+angle ROP = 180*
2x+ angle ROP=180*
2x +160*= 180*
2x=180*-160*
2x=20*
x=10*

So angle OPR= 10*