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

1 Answer
Ananda Dasgupta · sankarankalyanam
Feb 28, 2018

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

Explanation:

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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^@#

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