Question

Please answer, i will give 20 points!!!

Answer 1

5) x = 36°

7) x = 108°, y = 36°

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°

Answer 2

36

Explanation:

Pentagon has 5 sides

The formula for finding the sum of the measure of the interior angles is (n - 2) * 180

(5-2)×180= 3×180=540

To get each interior angles

540/5 = 108

180 -108 = 72

To get x

72+72+x= 180 (sum if angles in a triangle)

144+x= 180

x = 180 -144 = 36

2. x is part of the interior angles = 108