Answer:
m∠Z = 150°
Explanation:
This shape is an irregular pentagon, meaning its interior angles still sum to that of a normal pentagon (one in which all angles are equal).
You can calculate the sum of the interior angles for any polygon with the following formula:
(n - 2) * 180° where n is the number of sides.
We have a pentagon so our shape has 5 sides.
(n - 2) * 180° = (5 - 2) * 180° = 3 * 180° = 540°
Now that we know that interior angle sum, we can form an equation with the unknown angles on one side, and 540° on the other side.
(x) + (x - 4) + (2x + 14) + (x + 12) + (3x - 26) = 540°
Simplify, and solve for x.
8x - 4 = 540
8x = 544
x = 68°
The question asks for m∠Z so we substitute 68° for x in ∠Z's expression.
2(x) + 14 = 2(68) + 14 = 136 + 14 = 150°
Therefore, m∠Z = 150°