Question

In the diagram below, AB and bc are tangent to o. What is the measure of ac?

Answer 1

Answer:

Option D. $150\°$

Step-by-step explanation:

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

$m\angle ABC=\frac{1}{2}[arc\ ADC-arc\ AC]$

substitute the given values

$30\°=\frac{1}{2}[210\°-arc\ AC]$

$60\°=[210\°-arc\ AC]$

$arc\ AC=210\°-60\°=150\°$

Answer 2

Answer:

Option (D) is correct.

Step-by-step explanation:

OA is perpendicular to AB

OC is perpendicular to BC

Radius from the center is perpendicular to the tangent.

In quadrilateral ABCO,

∠ABC+∠BCO+∠AOC+∠OAB=360°

30°+90°+∠AOC+90°=360°

∠AOC+210°=360°

∠AOC=360°-210°

∠AOC=150°

Hence, arc AC=150°

Thus, the correct answer is option (D)