Answer:
Option D is correct
[tex]\angle E = 32^{\circ}[/tex]
Step-by-step explanation:
In the given diagram below DE and EF are tangent to O.
Join the point D and O and O and F as shown below.
It is given that:
[tex]\text{arc(DF)} = \angle DOF[/tex]
⇒[tex]148^{\circ} = \angle DOF[/tex]
or
[tex]\angle DOF = 148^{\circ}[/tex]
A line is tangent to circle if and only if the line is perpendicular to the radius drawn to the point of tangency.
Since, DE and EF are tangent
then:
[tex]\angle ODE = \angle OFE = 90^{\circ}[/tex]
In a quadrilateral EDOF:
Sum of all the angles add up to 360 degree.
[tex]\angle FED +\angle ODE + \angle DOF+ \angle OFE = 360^{\circ}[/tex]
Substitute the given values we have;
[tex]\angle FED +90^{\circ}+ 148^{\circ} +90^{\circ} = 360^{\circ}[/tex]
⇒[tex]\angle FED + 328^{\circ} = 360^{\circ}[/tex]
Subtract 328 degree from both sides we have;
[tex]\angle FED = 32^{\circ}[/tex]
Therefore, the measure of angle E is, 32 degree.
