Question

19. In the accompanying diagram, parallel lines AB and CD are intersected by transversal overline EF at G and H, respectively. If m angle BGH = 3x - 5 and m angle GHD = 6x + 14 what is the value of x?

Answer 1

To find the value of x, the equation 3x - 5 = 6x + 14 is solved, leading to x being equal to -19/3 or approximately -6.33, as the angles BGH and GHD are congruent due to alternate interior angle theorem.

Step-by-step explanation:

The student's question involves finding the value of x when given two angles formed by a transversal intersecting two parallel lines. When lines are parallel and intersected by a transversal, alternate interior angles are congruent, meaning they have equal measures.

Therefore, we can set the measure of angle BGH, 3x - 5, and the measure of angle GHD, 6x + 14, equal to each other and solve for x.

To find the value of x, we set up the equation 3x - 5 = 6x + 14.

Subtract 3x from both sides to get -5 = 3x + 14.

Then subtract 14 from both sides to get -19 = 3x.

Divide both sides by 3 to get x = -19 / 3.

We find that the value of x is -19/3 or approximately -6.33.