Question

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Explanation:

Step1: Find $x$ using exterior - angle property

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

Step2: Find $y$ using angle - sum property of a triangle

For the middle triangle, the sum of interior angles is $180^{\circ}$. One angle is $64^{\circ}$ and another is $x = 11^{\circ}$. So, $y=180^{\circ}-64^{\circ}-11^{\circ}=105^{\circ}$.

Step3: Find $z$ using linear pair

$y$ and $z$ form a linear pair. Since a linear pair of angles sums to $180^{\circ}$, $z = 180^{\circ}-y$. Substituting $y = 105^{\circ}$, we get $z=75^{\circ}$.

Answer:

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