To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).

To solve this equation, isolate the variable for which you are solving (c) on one side of the equation and put everything else on the other side.

3c + 6y = -5c - y + 4
3c = -5c - y + 4 - 6y
3c + 5c = -y + 4 - 6y
8c = -7y + 4
c = \( \frac{-7y + 4}{8} \)
c = \( \frac{-7y}{8} \) + \( \frac{4}{8} \)
c = -\(\frac{7}{8}\)y + \(\frac{1}{2}\)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

-6y - 2 = 7 - 4y
-6y = 7 - 4y + 2
-6y + 4y = 7 + 2
-2y = 9
y = \( \frac{9}{-2} \)
y = -4\(\frac{1}{2}\)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 57° - 59° = 64°

So, d° = 59° + 64° = 123°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 57° = 123°