Question

what is the value of p?
w+30°
20w
p
30w - 15°
p = \boxed{\circ}

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles:
$$30w - 15^\circ = (w + 30^\circ) + 20w$$

Step2: Simplify and solve for $w$

Combine like terms and isolate $w$:
$$30w - 15 = 21w + 30$$
$$30w - 21w = 30 + 15$$
$$9w = 45$$
$$w = 5$$

Step3: Find $p$ using supplementary angles

$p$ and $30w-15^\circ$ form a straight angle (sum to $180^\circ$):
$$p = 180^\circ - (30w - 15^\circ)$$
Substitute $w=5$:
$$p = 180 - (30\times5 - 15)$$
$$p = 180 - (150 - 15)$$
$$p = 180 - 135$$

Answer:

$45^\circ$