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In the figure, ABCD is a cyclic quadrilateral, O is the centre of the circle. If $∠ B O D = 160 °,$ then the measure of $∠ B P D$ is

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140 °

130 °

120 °

100 °

answer is D.

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Detailed Solution

B A D = \frac{1}{2} B O D = 80 °

ABPD is cyclic quadrilateral so

$B A D + B P D = 180 °$

$B P D = 180 ° - 80 ° = 100 °$

$B P D = 100 °$

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