Question

In the diagram below de and ef are tangent to o what is the measure of E

Answer 1

Answer: 32

Step-by-step expanation:

Answer 2

Answer:

Option D is correct

$\angle E = 32^{\circ}$

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:

$\text{arc(DF)} = \angle DOF$

⇒$148^{\circ} = \angle DOF$

or

$\angle DOF = 148^{\circ}$

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:

$\angle ODE = \angle OFE = 90^{\circ}$

In a quadrilateral EDOF:

Sum of all the angles add up to 360 degree.

$\angle FED +\angle ODE + \angle DOF+ \angle OFE = 360^{\circ}$

Substitute the given values we have;

$\angle FED +90^{\circ}+ 148^{\circ} +90^{\circ} = 360^{\circ}$

⇒$\angle FED + 328^{\circ} = 360^{\circ}$

Subtract 328 degree from both sides we have;

$\angle FED = 32^{\circ}$

Therefore, the measure of angle E is, 32 degree.