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

-4b + z = -3
z = -3 + 4b

then substitute the result (-3 - -4b) into the second equation:

-b + 2(-3 + 4b) = 8
-b + (2 x -3) + (2 x 4b) = 8
-b - 6 + 8b = 8
-b + 8b = 8 + 6
7b = 14
b = \( \frac{14}{7} \)
b = 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° - 46° - 54° = 80°

So, d° = 54° + 80° = 134°

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° - 46° = 134°

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

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 = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

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 = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)