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.

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 7cm + 11cm + 10cm = 28cm

The formula for circumference is circle diameter x π. Circle diameter is 2 x radius:

c = πd
c = π(2 * r)
c = π(2 * 5)
c = 10π

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

a² - 70 = a + 2
a² - 70 - 2 = a
a² - a - 72 = 0
a² - a - 72 = 0

Next, factor the quadratic equation:

a² - a - 72 = 0
(a + 8)(a - 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 8) or (a - 9) must equal zero:

If (a + 8) = 0, a must equal -8
If (a - 9) = 0, a must equal 9

So the solution is that a = -8 or 9

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° - 38° - 31° = 111°

So, d° = 31° + 111° = 142°

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° - 38° = 142°