Find m F. F
x+ 14
DT
\10x-9
58°
A) 23°
C) 29°
E
B) 27°
D) 81°

The correct option is A:

A) 23°

Step-by-step explanation:

Consider the line FV which is getting intersected by the segment DE, which divided the angle <EDV and <EDF with the line

We know that a straight line has an angle of 180°. Hence, the sums of angles which are formed due to the intersection of the segment DE, should be equal to 180°

<EDV + <EDF = 180°

<EDV + 10x - 9 = 180°

<EDV = 180 - 10x + 9

We know the sum of angles of the triangle is also 180°

<F + <EDV + <E = 180°

(x + 14) + (180 - 10x + 9) + 58  = 180

-9x + 261 = 180

-9x = -81

x = 9

As

<F = x + 14

Substitute x = 9

<F = 23°

the distance from any point on the parabola to the focus is the exact same as the distance from that point to the directrix.

if you could provide answer choices that might allow me to answer the question easier if my above answer isn't an option! (: