Question

what is the value of y? (hint: you will need to solve for x first)
triangle with angles 72°, (9y + 1)°, and (7x + 3)°, and an exterior angle (3x + 5)°

Explanation:

Step1: Set vertical angles equal

$7x + 3 = 3x + 5$
Solve for $x$: $7x - 3x = 5 - 3$ → $4x = 2$ → $x = 0.5$

Step2: Calculate angle for $y$

$3x + 5 = 3(0.5) + 5 = 1.5 + 5 = 6.5^\circ$ (vertical angle)
Triangle angles sum to $180^\circ$: $72 + 6.5 + (9y + 1) = 180$
Simplify: $79.5 + 9y = 180$ → $9y = 100.5$ → $y = \frac{100.5}{9} ≈ 11.17$ (or exact $\frac{67}{6}$)

Answer:

$\frac{67}{6}$ (or approximately 11.17)