The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

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° - 67° - 63° = 50°

So, d° = 63° + 50° = 113°

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° - 67° = 113°

A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.

You need to find the value of a so solve the first equation in terms of z:

8a + z = 7
z = 7 - 8a

then substitute the result (7 - 8a) into the second equation:

5a - 5(7 - 8a) = -1
5a + (-5 x 7) + (-5 x -8a) = -1
5a - 35 + 40a = -1
5a + 40a = -1 + 35
45a = 34
a = \( \frac{34}{45} \)
a = \(\frac{34}{45}\)

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -56 as well and sum (Inside, Outside) to equal 1. For this problem, those two numbers are -7 and 8. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + y - 56
y² + (-7 + 8)y + (-7 x 8)
(y - 7)(y + 8)