In the figure below,

Question

and segments

,

, and

intersect at point
.

The angles formed by the intersecting lines in the clockwise direction are angle C-G-A, angle A-G-E, angle E-G-D, angle D-G-B, angle B-G-F, and angle F-G-C. The angle C-G-E is 90 degrees and is divided into angle C-G-A, and angle A-G-E. The angle C-G-A is 51 degrees and is vertically opposite to angle D-G-B. The angle D-G-F is divided into angle D-G-B and angle B-G-F. And angle B-G-F is marked as 'x' and it is vertically opposite to angle A-G-E.

What is the value of x?
Responses

39

39 °

45

45 °

49

49 °

51

51 °

Answer 1

To find the value of \( x \), we start by noting the relationships among the angles described in the problem.

1. Given Angles:

   • \( \angle C-G-E = 90^\circ \)
   • \( \angle C-G-A = 51^\circ \) (given)
   • \( \angle D-G-B = 51^\circ \) (vertically opposite to angle \( \angle C-G-A \))

2. Calculate \( \angle A-G-E \):

   • Since \( \angle C-G-E = \angle C-G-A + \angle A-G-E \): \[ 90^\circ = 51^\circ + \angle A-G-E \] \[ \angle A-G-E = 90^\circ - 51^\circ = 39^\circ \]

3. Relationship with \( x \):

   • Since \( \angle A-G-E \) (39°) is vertically opposite to \( \angle B-G-F \) (which is marked as \( x \)): \[ \angle B-G-F = 39^\circ \]

Thus, the value of \( x \) is 39°.

The answer is therefore: 39 °