Question

find the values of x and y.

x =

y =

(7y)°
(x + 2)°
82°

Explanation:

Step1: Use angle - sum property of a right - angle

The sum of the angles around a point is 360°. Here, we see a right - angle (90°) and other angles. The angle formed by the lines is a right - angle, and we know that the sum of the two non - right angles adjacent to the right - angle is 90°. So, we set up the equation for the non - right angles: $(x + 2)+7y=90$.

Step2: Solve for $x$ in terms of $y$ (not necessary in this case, we can also solve directly).

We know that we need to find integer values for $x$ and $y$ that satisfy the equation. Let's assume we first solve for $x$: $x=90 - 2-7y=88 - 7y$.
We can also try some simple values. Since the angles are positive, we know that $x+2>0$ and $7y>0$.
Let's assume we start with $y = 12$. Then $7y=84$.
Substitute $7y = 84$ into the equation $(x + 2)+7y=90$.
We get $x+2+84 = 90$.

Step3: Solve for $x$

$x+86=90$, so $x=90 - 86=4$.
If $7y = 84$, then $y=\frac{84}{7}=12$.

Answer:

$x = 4$
$y = 12$