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° - 20° - 46° = 114°

So, d° = 46° + 114° = 160°

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° - 20° = 160°

You need to find the value of c so solve the first equation in terms of x:

-6c + x = 6
x = 6 + 6c

then substitute the result (6 - -6c) into the second equation:

-6c - 7(6 + 6c) = -5
-6c + (-7 x 6) + (-7 x 6c) = -5
-6c - 42 - 42c = -5
-6c - 42c = -5 + 42
-48c = 37
c = \( \frac{37}{-48} \)
c = -\(\frac{37}{48}\)

The sum of the interior angles of a triangle is 180°:
180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 56° - 30° = 94°

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 + 9a - 30 = 5a + 2
a² + 9a - 30 - 2 = 5a
a² + 9a - 5a - 32 = 0
a² + 4a - 32 = 0

Next, factor the quadratic equation:

a² + 4a - 32 = 0
(a - 4)(a + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 4) or (a + 8) must equal zero:

If (a - 4) = 0, a must equal 4
If (a + 8) = 0, a must equal -8

So the solution is that a = 4 or -8

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.