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°