Question

Help! What is the measure of AC?

Answer 1

A) 138 because 360 minus 90 plus 90 plus 42 is 138

Answer 2

Answer: 138°

Step-by-step explanation:

Since, by the Angles of Intersecting Chords Theorem, If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Here, by the diagram,

m∠DBE = 180° - m∠ABD ( Linear pair )

⇒ m∠DBE = 180° - 90° = 90°

Thus, by the above theorem,

$\frac{1}{2}[m(\widehat{AC})+m(\widehat{DE})]=m\angle D BE$

$\implies \frac{1}{2}[m(\widehat{AC})+42^{\circ}]=90^{\circ}$

$\implies m(\widehat{AC})+42^{\circ}=180^{\circ}$

$\implies m(\widehat{AC})=180^{\circ}-42^{\circ}=138^{\circ}$

Hence, the measurement of arc AC = 138°

⇒ Option A is correct.