Question

if the centre is O find the value of x

Answer 1

It is known that the angel subtended by the diameter on a circle is 90° (because the angle subtended by an arc at the center of a circle is twice the angle subtended by it on the circle ; here angle subtended at the centre is 180°, therefore angle subtended on the circle will be 180°/2 i.e. 90°)
Therefore angle CED = 90.
Then angle OED= 90°-40°=50°........ (1)
Also, in triangle DOE
DO=EO=r (radii of the same circle)
=> angle ODE = angle OED ( angle opposite to equal sides in a triangle are equal)
Hence, x = angle ODE = angle OED = 50° (using 1)


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