Question

1 po
13. The measure of the angle
ADC is degree.
is cyclic.
B
A А
30
60
D​

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°