Answer:
(d) z = 27
Explanation:
You want the value of z where one interior angle of a regular pentagon has the measure (2z +54)°.
Interior angles
The measure of an interior angle of a regular n-gon is ...
a = 180° -360°/n
For n=5, this is ...
a = 180° -360°/5 = 180° -72° = 108°
The problem statement tells us this is equal to the given angle expression:
108° = (2z +54)°
54 = z +27 . . . . . . . . divide by 2°
27 = z . . . . . . . . . . . subtract 27
The value of z is 27.
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Additional comment
We used the fact that exterior angles of a convex polygon total 360°, and the adjacent interior angle is the supplement of that. The angle expression is often expressed as the total of interior angles being ...
180°(n -2) . . . sum of interior angles of n-gon
The angles of a regular polygon are congruent. Since we want one of those angles, we can divide by n. When we do that, we get the expression above.
The equation for the angle value is a "2-step" equation. The usual procedure for solving it is to subtract the unwanted constant (54), then divide by the coefficient of the variable. Here, we observed that all of the numbers had that coefficient (2) as a factor, so we chose to do the division first. This makes the numbers smaller and perhaps easier to work with mentally.