Question

find the value of x
challenge: find the value of y.

Explanation:

Step1: Use exterior angle property (top)

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
$$127^\circ = 87^\circ + x^\circ$$

Step2: Solve for x

Rearrange to isolate x.
$$x = 127 - 87 = 40$$

Step3: Find interior angle (bottom)

The angle adjacent to $123^\circ$ is supplementary.
$$180^\circ - 123^\circ = 57^\circ$$

Step4: Use exterior angle property (bottom)

The labeled exterior angle equals the sum of the two non-adjacent interior angles.
$$18y + 11 = 57 + 4y + 7$$

Step5: Simplify and solve for y

Combine like terms and isolate y.
$$18y - 4y = 57 + 7 - 11$$
$$14y = 53$$
$$y = \frac{53}{14} \approx 3.79$$

Answer:

$x = 40$, $y = \frac{53}{14}$ (or approximately $3.79$)