Question

!50 POINTS! (2 SIMPLE GEOMETRY QUESTIONS)

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Answer 1

1) 15

2)

1) d) 120

2) a) 90

3) b) 72

4) e) 60

Explanation:

1) interior angle = 165

exterior angle = 180 - interior

= 180 - 165

= 15

2) Measure of one exterior angle of a polygon with n sides is :
`(360)/(n)`

1) triangle : 3 sides

exterior = 360/3 = 120

2) quad : 4 sides

exterior = 360/4 = 90

3) pentagon : 5 sides

exterior = 360/5 = 72

4) hexagon : 6 sides

exterior = 360/6 = 60

Answer 2

The measure of the exterior angle is 15°.

1) d. 120°

2) a. 90°

3) b. 72°

4) e. 60°

Explanation:

The sum of an interior and exterior angle of a polygon is 180°.

Therefore, to find the measure of an exterior angle, subtract the interior angle from 180°:

`\textsf{Exterior\;angle}=180^(\circ)-165^(\circ)=15^(\circ)`

Therefore, the measure of the exterior angle is 15°.

`\hrulefill`

The formula for calculating the size of an exterior angle of a polygon with n sides is:

`\boxed{\textsf{Exterior angle of a polygon} = (360^(\circ))/(n)}`

1. A triangle has 3 sides, so n = 3. Therefore:

`\textsf{Exterior angle of a triangle} = (360^(\circ))/(3)=120^(\circ)`

2. A quadrilateral has 4 sides, so n = 4. Therefore:

`\textsf{Exterior angle of a quadrilateral} = (360^(\circ))/(4)=90^(\circ)`

3. A pentagon has 5 sides, so n = 5. Therefore:

`\textsf{Exterior angle of a pentagon} = (360^(\circ))/(5)=72^(\circ)`

4. A hexagon has 6 sides, so n = 6. Therefore:

`\textsf{Exterior angle of a hexagon} = (360^(\circ))/(6)=60^(\circ)`

Solution:

1. d. 120° Triangle
2. a. 90° Quadrilateral
3. b. 72° Pentagon
4. e. 60° Hexagon