Can u guys show me how u got the answers?

What are some ways to remember postulates in geometry?

shusha [124]

I took five years before and it was hard for me to remember the postualates. I found it helpful to practice proving problems that involved the postualate. Some postualates like SAS are just abbreviations. SAS- Side-Angle-Side

7 0

3 years ago

8-35. Use your knowledge of polygons to answer the questions below, if possible.

Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is $1980^0$

Then:

$(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13$

The polygon has 13 sides.

II. If the Interior angle is $900^0$

Then:

$(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7$

The polygon has 7 sides.

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: $\frac{360^0}{n}$

If the exterior angle of a regular polygon is 90°

Then:

$90\°=\frac{360^0}{n}\\ 90n=360\\n=4$

The regular polygon has 4 sides and it is called a Square.

(c)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is: $\frac{(n-2)180^0}{n}$

For a pentagon, n=5

Then:

$\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0$

(d)The sum of the exterior angle of a polygon is 360 degrees.

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

$57+74+56+66+x=360^0\\253+x=360\\x=107^0$

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180= $1620^0$

The sum of the interior angle does not change either in a regular or irregular polygon.

3 0

2 years ago

Stephanie had a total of 80 pieces of $ 2 and $ 10 notes. After spending 2/5 of her $ 2 notes and 8 pieces of her $ 10 notes, sh

Ghella [55]

Answer:

$440

Step-by-step explanation:

notes $2 - n

notes $10 - m

n + m = 80 ----------> m = 80 - n

1 - 2/5 = 3/5

$\frac{3}{5} * n = m - 8$

$\frac{3}{5} * n = 80 - n - 8 \\\\\frac{3}{5} * n + n = 72\\\\\frac{8}{5} * n = 72\\n = 45 \\m = 35\\$

45 * $2 + 35 * $10 = 90 + 350 = $440

3 0

3 years ago

(ASAP) Solye for n. 24 = 3(n – 5) n=

Paul [167]

Answer: can u check out the image cuz the answer is in the photo and hope this helps can u give me brainliest

Step-by-step explanation:

24=3(n-5)

Distribute.

24=3(n) + 3(-5)

24 = 3n -15

Add 15 to both sides.

39 = 3n

Divide both sides by 3.

n = 13.

I hope this helps!.

6 0

2 years ago

Solve the inequality. 3x + 5 ———- <4 2 x < [?]

astra-53 [7]

Answer:

$x \leqslant 1$

Step-by-step explanation:

first multiply both side by 2 to get rid of the fraction

$3x + 5 \leqslant 4(2)$

$3x + 5 \leqslant 8$

$3x \leqslant 8 - 5$

$3x \leqslant 3$

$x \leqslant 1$

3 0

2 years ago