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I will give brainliest Given ⊙N, what is mABC ?

A circle with center point N and three points A, B, C on its circumference. A line is drawn connecting the points A, N and C and the angle ANC is given as 138 degree.

A. 111°
B. 138°
C. 222°
D. 276°

I will give brainliest Given N what is mABC A circle with center point N and three points A B C on its circumference A line is drawn connecting the points A N a class=

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sqdancefan

9514 1404 393

Answer:

  138°

Step-by-step explanation:

The measure of arc ABC is the measure of the corresponding central angle, ∠ANC. That angle is shown as 138°, so the measure of arc ABC is 138°.

Measure of an angle  ABC is 111 degrees i.e. [tex]m[/tex]∠ABC = 111 degrees.

Angle subtended by an Arc of a circle-Theorem

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

According to the given question

The angle subtended at the center of circle, i.e. ∠ANC = 138 degrees.

The exterior angle at the center is (360 - 138)degrees = 222 degrees

by angle subtended by an Arc of a circle theorem

[tex]m[/tex]∠ABC = [tex]\frac{222}{2}[/tex] [tex]= 111 degrees[/tex]

Hence, [tex]m[/tex]∠ABC = 111 degrees.

Learn more about angle subtended at the center of circle theorem here:

https://brainly.com/question/2506683

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