Answer: D. [tex]29^{\circ}[/tex]
Step-by-step explanation:
- The secant angle is exactly half of the difference between the measure of the two arcs formed by it . (1)
In the given picture , we can see that the ∠ ACE is an Secant angle.
Two arcs = arcBD and arcAE
Now , by considering (1) , we have
[tex]\angle{ACE}=\dfrac{1}{2}(\overarc{AC}-\overarc{BD})\\\\\Rightarrow\ \angle{ACE}=\dfrac{1}{2}(106^{\circ}-48^{\circ})\\\\\Rightarrow\ \angle{ACE}=\dfrac{1}{2}(58^{\circ}))\\\\\Rightarrow\ \angle{ACE}=29^{\circ}[/tex]
Hence, the measure of [tex]\angle{ACE}=29^{\circ}[/tex]
hence, the correct answer is D. [tex]29^{\circ}[/tex]
