O is the centre of the circle prove that
angle x+ angle y= angle z
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proof
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AB is a chord of the circle. Chord AB makes an angle at the center which is twice the angle it makes at a point on the circumference.
hence w = v = x/2
in the quadrilateral, CGDH,
angle C = y (vertical angle)
sum of angles in the quadrilateral CGDH is
180 - v + y + 180 - w + z = 360
hence, w + v = x = y + z
.......................................
AB is a chord of the circle. Chord AB makes an angle at the center which is twice the angle it makes at a point on the circumference.
hence w = v = x/2
in the quadrilateral, CGDH,
angle C = y (vertical angle)
sum of angles in the quadrilateral CGDH is
180 - v + y + 180 - w + z = 360
hence, w + v = x = y + z
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