Final answer:
The measure of interior angle ∣X is 58°, and its exterior angle is 122°. This was found by setting up an equation based on the exterior angle theorem and solving for the variable g.
Step-by-step explanation:
To solve for the measure of °X and its exterior angle given the equations m∣X = (2g + 16)° and the exterior angle to ∣X measures (4g + 38)°, we can use the fact that the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
As we have an additional condition that the interior angle = 122°, which seems to be a misplaced fact and not relevant to our calculation, we will focus on the given equations for the angles related to ∣X.
From the properties of triangles, we know that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles.
Since we have only one interior angle for ∣X and its measure given by m∣X, and its relative exterior angle given, we can set up an equation:
(2g + 16)° + (4g + 38)° = 180° (sum of the interior angle and its adjacent exterior angle for a straight line which is 180 degrees).
Simplify and solve the equation:
6g + 54 = 180°
6g = 126°
g = 21°
Now we substitute the value of g into the original equations to find m∣X and the exterior angle:
m∣X = (2(21) + 16)°
= 58°
Exterior angle = (4(21) + 38)°
= 122°
Hence, the measure of interior angle ∣X is 58°, and its exterior angle is 122°.