Find m Give explanation please

m < FGN = 88°

Step-by-step explanation:

The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles (also known as remote interior angles).

Given the exterior angle, m <FGN = (7x + 18)°, and the two remote interior angles, m < E = 38° and m < F = (6x - 10)°:

The following equality statement can be established according to the exterior angle theorem:

m < E  + m < F  = m <FGN

38 + 6x - 10 = 7x + 18

Combine like terms:

28 + 6x = 7x + 18

Subtract 6x from both sides:

28 + 6x - 6x = 7x - 6x + 18

28 = x + 18

Subtract 18 from both sides:

28 - 18 = x + 18 - 18

10 = x

Next, substitute the value of x = 10 into the equality statement to determine whether it is the correct value of x, and to find the measures of < FGE and < F.

m < E  + m < F  = m <FGN

38° + (6x - 10)° = (7x + 18)°

38 + 6(10) - 10 = 7(10) + 18

38 + 60 - 10 = 70 + 18

88 = 88 (True statement).

Therefore, m < FGN = 88°

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

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step-by-step explanation: