Answer:
x° = 36°, y° = 36°, z° = 72°
Step-by-step explanation:
Each interior angle of a regular polygon is given by the following formula;
Interior angle = (n - 2)×180°/n
Where;
n = The number of sides on the polygon
For the pentagon, we have;
n = 5, therefore;
Interior angle = (5 - 2)×180°/5 = 108°
ΔDCA is an isosceles triangle, with the segments CD and CA being equal, therefore;
∠ADC = ∠DAC = x°, and ∠ACD = 108°
Therefore
x° = (180° - 108°)/2 = 36°
x° = 36°
∠BAC = 2·x° + y° = 108°
∴ y° = 108° - 2·x° = 108° - 2 × 36° = 36°
y° = 36°
ΔADE is an isosceles triangle, with segments AD and AE equal, therefore, the base angles are z° each
Therefore, in ΔADE, we have;
z° = (180° - 36°)/2 = 72°
z° = 72°
