Question

NO LINKS!! URGENT HELP PLEASE!!!

Please help me with #6, 7, and 8.

Answer 1

Explanation:

6.

the sum of all internal angles in a polygon is

(n-2)×180

n is the number of sides of internal angles.

now, that means that one internal angle of a regular polygon is

(n-2)×180/n

and we know that is 170°.

so,

170 = (n-2)×180/n

170n = 180n - 360

-10n = -360

10n = 360

n = 36

the polygon has 36 sides.

7.

a. is a rectangle or a square, as the fact that all 4 segments of the diagonals are equally long solid to both. after all, a square is just a special rectangle.

but given the picture that suggests different Legrand and widths it is a rectangle.

b.

parallelogram.

the 2 lengths are equal, and the 2 widths are equal. and therefore, both lengths are parallel and both widths are parallel.

but the angles are not 90°. so, it is not a rectangle, but still a parallelogram.

c.

isoceles trapezoid.

top and bottom sides are parallel, but if different size.

the left and right sides are equally long and inclined inwards.

8.

as explained in 7. : the 2 lengths are equal and parallel, and the 2 widths are equal and parallel.

also the diagonals intercept each other at their midpoints. so, both segments of a diagonal are equal.

the sum of all angles is still 360°, and the opposing angles are equal, while every pair of neighboring angles are together 180°.

and - the sum of all angles in a triangle is always 180°.

a. AD = BC = 7

b. DC = AB = 16

c. AC = 2×EC = 2×7 = 14

d. EB = ED = 10.2

angle DAB = angle BCD = 120°

angle ADC = angle ABC = 43 + x

e.

180 = 120 + 43 + x

60 = 43 + x

17° = x

so,

angle ABC = angle ADC = 43 + 17 = 60°

f. angle CDB = x = 17°

g. angle CBD = angle ADB = 43°.

because

180 = CDB + BCD + CBD

180 = 17 + 120 + CBD

43° = angle CBD

h. angle BCD = angle DAB = 120°.

Answer 2

Question 6:

• The regular polygon has 36 sides.

Question 7:

• Shape a is a rectangle because the diagonals bisect each other and the length of the diagonals is equal.
• Shape b is a parallelogram because it has two pairs of parallel opposite sides.
• Shape c is an isosceles trapezoid because one pair of sides is parallel and the remaining sides are non-parallel and equal in length.

Question 8:

• AD = 7
• DC = 16
• AC = 14
• EB = 10.2
• m∠ABC = 60°
• m∠CDB = 17°
• m∠CBD = 43°
• m∠BCD = 120°

Explanation:

Question 6

The formula for calculating the interior angle of a regular polygon is:

`\text{Interior angle}=((n - 2) * 180^\circ)/(n)`

where n is the number of sides of the regular polygon.

To calculate the number of sides a regular polygon has if its interior angle is 170°, substitute this angle into the formula and solve for n.

`\implies 170^(\circ)=((n - 2) * 180^(\circ))/(n)`

`\implies 170n=180(n - 2)`

`\implies 170n=180n-360`

`\implies -10n=-360`

`\implies n=36`

Therefore, a regular polygon with an interior angle of 170° has 36 sides.

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Question 7

Congruent lines are shown by placing the same number of tick marks on each congruent line segment.

Parallel lines are shown by placing the same number of arrows on each parallel line.

Shape a is a rectangle because the diagonals bisect each other and the length of the diagonals is equal, indicated by the tick marks.

Shape b is a parallelogram because it has two pairs of parallel opposite sides.

Shape c is an isosceles trapezoid because one pair of sides is parallel and the remaining sides are non-parallel and equal in length.

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Question 8

A parallelogram has opposite sides that are of equal length. Therefore:

• AD = BC = 7

• DC = AB = 16

The diagonals of a parallelogram bisect each other. Therefore:

• EB = DE = 10.2
• AE = EC = 7

Therefore, AC = AE + EC = 7 + 7 = 14

Same-side interior angles sum to 180°. Therefore:

⇒ m∠DAB + m∠ABC = 180°

⇒ 120° + m∠ABC = 180°

⇒ m∠ABC = 60°

The opposite angles of a parallelogram are equal. Therefore:

• m∠BCD = m∠DAC = 120°
• m∠ADC = m∠ABC = 60°

As m∠ADC = 60° and m∠ADE = 43° then:

• m∠CDB = 60° - 43° = 17°

According to the alternate interior angles theorem:

• m∠CBD = m∠ADE = 43°