In a cyclic quadrilateral , angle a + angle b = 170 , angle b + angle c = 150 , what is angle d?

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Answer 1 · 2018-02-28T02:23:36

$color(green)(hat D = 110^@$

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Because ABCD is a cyclic quadrilateral, we have

$/_a+/_c =/_b+/_d = 180$

Given $/_a +/_b = 170$ and $/_b+/_c = 150$ , we have

$/_a+2/_b+/_c = 170+150 = 320 implies$

$2/_b = 320-180=140$ or $/_b = 70^@$

Hence, $/_d = 180-/_b = 180-70 = color (green)(110^@$