Question

what we have learned about triangle angle

Explanation:

Step1: Use exterior - angle property for right - hand triangle

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the right - hand triangle, $39^{\circ}=28^{\circ}+x^{\circ}$. Solving for $x$ gives $x = 39 - 28=11^{\circ}$.

Step2: Use angle - sum property for left - hand triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In the left - hand triangle, we know one angle is $64^{\circ}$, and we just found that the adjacent angle to $y$ is $x = 11^{\circ}$. So $y^{\circ}+64^{\circ}+11^{\circ}=180^{\circ}$. First, simplify the left - hand side: $y+75 = 180$. Then solve for $y$: $y=180 - 75 = 105^{\circ}$.

Step3: Use supplementary angles property

Since $y$ and $z$ are supplementary (they form a straight line), $y + z=180^{\circ}$. We know $y = 105^{\circ}$, so $z=180 - 105 = 75^{\circ}$.

Answer:

$x = 11^{\circ}$, $y = 105^{\circ}$, $z = 75^{\circ}$