Question

If arc AXC = 235°, what is m∠ABC? a. 117.5° b. 60° c. 55° d. 125°

Answer 1

Answer:

The correct option is c.

Step-by-step explanation:

Given information: The measure of arc AXC is 235°. Let the center of the circle be O.

The sum of all disjoint arcs is 360°. So,

$Arc(AXC)+Arc(AC)=360^{\circ}$

$235^{\circ}+Arc(AC)=360^{\circ}$

$Arc(AC)=360^{\circ}-235^{\circ}$

$Arc(AC)=125^{\circ}$

$\angle AOC=125^{\circ}$

The measure of arc AC is 125°.

Line BA and BC are tangent on the circle O from the same point, so the sum of opposite angles of the quadrilateral is 180°.

$\angle AOC+\angle ABC=180^{\circ}$

$125^{\circ}+\angle ABC=180^{\circ}$

$\angle ABC=180^{\circ}-125^{\circ}$

$\angle ABC=55^{\circ}$

The measure of angle ABC is 55°. Therefore the correct option is c.

Answer 2

He answer is C 55
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