The measures of the angles of a quadrilateral have sum \(\displaystyle 360^{\circ }\). If \(\displaystyle x\) is the measure of the unknown angle, then:

\(\displaystyle x + 51 + 120 + 77 = 360\)

\(\displaystyle x + 248 = 360\)

\(\displaystyle x + 248 -248 = 360-248\)

\(\displaystyle x = 112\)

The angle measures \(\displaystyle 112^{\circ }\).

The sum of the degree measures of the angles of a quadrilateral is 360, so we can set up and solve for \(\displaystyle x\) in the equation:

\(\displaystyle x + x + \left ( x+45 \right ) + \left ( x+65 \right ) = 360\)

\(\displaystyle 4x+110= 360\)

\(\displaystyle 4x+110- 110 = 360 - 110\)

\(\displaystyle 4x = 250\)

\(\displaystyle 4x\div 4 = 250 \div 4\)

\(\displaystyle x = 62.5\)

Given that there are 360 degrees when all the angles of a quadrilateral are added toghether, this problem can be solved with the following equation:

\(\displaystyle 360 = 79 +100 +50 + 2x\)

\(\displaystyle 360=229+2x\)

\(\displaystyle 131=2x\)

\(\displaystyle x=65.5\)

Given that there are 360 degrees when the angles of a quadrilateral are added together, it follows that:

\(\displaystyle 94 + 27+ 81 + 4x =360\)

\(\displaystyle 202+4x=360\)

\(\displaystyle 4x=158\)

\(\displaystyle x=39.5\)

Given that the perimeter is 86, the sides of the quadrilateral will all add up to this amount. 

\(\displaystyle 15+25+30+2x^{2}\cdot \frac{2}{x}=86\)

The first step is the add together all the integers. 

\(\displaystyle 70+2x^{2}\cdot \frac{2}{x}=96\)

Next, we subtract 70 from each side. 

\(\displaystyle 2x^{2}\cdot \frac{2}{x}=16\)

We reduce the left side of the equation:

\(\displaystyle 4x=16\)

Now, we divide each side by 4. This leaves:

\(\displaystyle x=4\)

The perimeter of a quadrilateral is the sum of the length of all four sides. In a square, each side is of equal length. Thus, the perimeter is the length of a side (given) times 4.

\(\displaystyle 17.5\times4=70\)

If the area of a square is \(\displaystyle 25x^{2}\), then the length of one side will be equal to the square root of \(\displaystyle 25x^{2}\). 

\(\displaystyle \sqrt{25x^{2}}=5x\)

The perimeter is equal to 4 times the length of one side. 

This gives us: \(\displaystyle 5x\cdot 4 = 20x\)

One of your holiday gifts is wrapped in a cube-shaped box. 

If one of the edges has a length of 6 inches, what is the perimeter of one side of the box? 

To find perimeter of a square, simply multiply the side length by 4

\(\displaystyle Perimeter_{square}=4*6in=24 in\)

Call the diameter of the circle \(\displaystyle d\). The length of each side of the square also is equal to this.

The diameter of the circle is equal to its circumference divided by \(\displaystyle \pi\), so

\(\displaystyle d = \frac{C}{ \pi} = \frac{30}{ \pi}\).

The perimeter of the square is four times this sidelength, so 

\(\displaystyle P= 4d = 4 \cdot \frac{30 }{\pi} = \frac{120}{\pi}\).

To find the perimeter of a square, we will use the following formula:

\(\displaystyle \text{perimeter of square} = a+b+c+d\)

where a, b, c, and d are the lengths of the sides of the square.

Now, we know the width of the square has a length of 4cm.  Because it is a square, all sides are equal.  Therefore, all sides are 4cm.

Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{perimeter of square} = 4\text{cm} +4\text{cm} +4\text{cm} +4\text{cm}\)

\(\displaystyle \text{perimeter of square} = 16\text{cm}\)