Question

A circle is centered on point BBB. Points AAA, CCC and DDD lie on its circumference. If \orange{\angle ADC}?ADCstart color orange, angle, A, D, C, end color orange measures 35^\circ35 ? 35, degree, what does \blue{\angle ABC}?ABCstart color blue, angle, A, B, C, end color blue measure?

Answer 1

Answer: 70

Step-by-step explanation: Khan Academy

Answer 2

∠ABC=
`70^0`

Explanation:

In the attached diagram,

If Angle ADC =
`35^0`

Since the center of the circle is at B

∠ABC is the angle subtended at the center by arc AC.

∠ADC is the angle subtended at the circumference by arc AC.

Theorem

The angle subtended by an arc at the center of a circle is double the size of the angle subtended by the same arc at the circle's circumference.

Therefore by the theorem above

∠ABC = 2 X ∠ADC

=2 X 35

∠ABC=
`70^0`