Question

What is the measure of ACE shown in the diagram below

Answer 1

D

Explanation:

∠ACE is a secant- secant angle and is measured as half the difference of the intersecting arcs, that is

∠ACE = 0.5(m AE - m BD )

= 0.5 (106 - 48)° = 0.5 × 58° = 29° → D

Answer 2

Answer: D.
`29^(\circ)`

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

`\angle{ACE}=(1)/(2)(\overarc{AC}-\overarc{BD})\\\\\Rightarrow\ \angle{ACE}=(1)/(2)(106^(\circ)-48^(\circ))\\\\\Rightarrow\ \angle{ACE}=(1)/(2)(58^(\circ)))\\\\\Rightarrow\ \angle{ACE}=29^(\circ)`

Hence, the measure of
`\angle{ACE}=29^(\circ)`

hence, the correct answer is D.
`29^(\circ)`