Answer:
5) x = 36°
7) x = 108°, y = 36°
Step-by-step explanation:
5) The exterior angle at any vertex of a regular polygon has measure 360°/n, where n is the number of sides of the polygon. Here, the external angle is ...
360°/5 = 72°
The isosceles triangle with x as its vertex angle has base angles that are both 72°, so x is ...
x + 72° +72° = 180°
x = 36° . . . . . . . . . . . subtract 144° from both sides
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7) In (5), we found the external angle at the vertex of a regular pentagon to be 72°. Then the internal angle (x, here) is ...
x = 180° -72°
x = 108°
Angle y is the base angle of an isosceles triangle with vertex angle 108°, so its measure will be ...
y + y + 108° = 180°
2y = 72°
y = 36°
