Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
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Answer 1

1st picture:

• 9 sides

2nd Picture:

• 30 feet,

3rd picture:

• x=6

Explanation:

For 1st picture:

Given:

Interior angle of a regular polygon = 140°

To find:

no. of side=?

Solution:

The formula for the sum of the interior angles in a polygon is:

`\boxed{\tt (sum\: of\:interior\:\:angle=(n - 2)*180^o}`

• where n is the number of sides in the polygon.

Since we know that the measure of one interior angle is 140°, we can set up the following equation:

sum of interior angle= n*interior angle of a regular polygon

Now, Substituting value in above formula, we get,

140n = 180(n - 2)

opening bracket

140n =180n-360

Solving for n, we get:

180n-140n=360

40n=360

n=360/40

n=9

Therefore, the polygon has 9 sides.

`\hrulefill`

For 2nd Question:

Given:

Hypotenuse = 34 ft

Perpendicular = 16 ft

Base=?

We can use Pythagoras theorem to find the value of base.

so, we have,

`\boxed{\tt Hypotenuse^2=base^2+Perpendicualr^2}}`

substituting value:

`\tt 34^2=base^2+16^2`

solving for base², we get

`\tt Base^2=34^2-16^2\\Base^2=900`

doing square root on both side,we get

`\tt Base=√(900)\\\tt Base=30`

Therefore, Rebecca's yard's wide is 30 feet,

`\hrulefill`

For 3rd question:

(5x-1)°=(3x+11)° Being alternate interior angle

5x-1=3x+11

adding both side by 1.

5x=3x+11+1

5x=3x+12

subtracting both side by 3x.

5x-3x=12

2x=12

dividing both side by 2.

`\tt (2x)/(2)=(12)/(2)`

x=6

therefore, the value of x is 6.