Question

1. find x and y.

Explanation:

Step1: Find the interior - angle adjacent to 140°

The sum of an exterior angle and its adjacent interior - angle of a triangle is 180°. Let the interior - angle adjacent to 140° be $z$. Then $z + 140^{\circ}=180^{\circ}$, so $z = 180^{\circ}-140^{\circ}=40^{\circ}$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the given triangle, we know one angle is 28° and another is $z = 40^{\circ}$. Let's find $y$.
We have $28^{\circ}+y + 40^{\circ}=180^{\circ}$.
First, simplify the left - hand side: $68^{\circ}+y = 180^{\circ}$.
Then, solve for $y$: $y=180^{\circ}-68^{\circ}=112^{\circ}$.

Step3: Find $x$

Since the sum of the interior angles of a triangle is 180°, and we know two angles of the larger triangle formed (28° and $y = 112^{\circ}$), and $x$ is the third angle.
$x=180^{\circ}-(28^{\circ}+112^{\circ})=40^{\circ}$.

Answer:

$x = 40^{\circ}$, $y = 112^{\circ}$