Question

what are the values of p and x?
2p
4p
x
3p - 27°
p =
x =

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles, so:
$$4p = 2p + (3p - 27)$$

Step2: Simplify and solve for p

Combine like terms and isolate p:
$$4p = 5p - 27$$
$$27 = 5p - 4p$$
$$p = 27$$

Step3: Solve for x using linear pair

$4p$ and $x$ form a linear pair (sum to $180^\circ$):
$$x = 180 - 4p$$
Substitute $p=27$:
$$x = 180 - 4\times27$$
$$x = 180 - 108$$
$$x = 72$$

Answer:

$p = 27^\circ$
$x = 72^\circ$