Question

8. In the given figure, find the measure of the
angles ZAOC, ZCOE, ZEOF and ZBOD.
A
B.
80°
C С
D
0
70°
E
F​

Answer 1

Answer:

Given that: ABCD is a cyclic quadrilateral

∠DCB=82°

∠DCA=46°

∠CYB=62°

∠ACB=∠DCB−∠DCA=82−46=36°

Consider △CYB

∠CBY=180°−∠BCY−∠CYB=180°−62°−36°=82° (sum of three angles of a triangle is 180°)

Also, ∠ACD=∠ABD=46° ......... (angles in the same segment)

Thus, ∠ABC=∠ABD+∠CBY=(82+46)°=128°

Answer: ∠ABC=128°

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