Final answer:
To find the measure of the external angle of a polygon with interior angles (7x – 16)°, use the relationship that the sum of the internal and external angles of a polygon is 180° to get the external angle measure as (196 – 7x)°.
Step-by-step explanation:
To find the measure of the external angle of a polygon with interior angles given by the expression (7x – 16)°, we use the fact that the sum of the measures of an external angle and its corresponding internal angle is equal to 180°. Since the problem provides the expression for the interior angle, we set up the equation:
Interior angle + External angle = 180°
(7x – 16)° + External angle = 180°
Solving for the external angle, we subtract the expression for the interior angle from 180°:
External angle = 180° – (7x – 16)°
External angle = 180° – 7x + 16°
External angle = (196 – 7x)°
Therefore, the measure of the external angle is (196 – 7x)°.