Let's solve the questions step by step:

(a) Solve for $\angle y$:

• The given figure has a right angle (90°) and another angle of 56°.
• The sum of angles around a point on a straight line is $180^\circ$.

$\angle y + 90^\circ + 56^\circ = 180^\circ$

$\angle y = 180^\circ - 90^\circ - 56^\circ = 34^\circ$

$\boxed{\angle y = 34^\circ}$

(b) Solve for $\angle ABD$:

• At point $B$, the angles given are $125^\circ$ and $119^\circ$.
• The sum of angles around a point is $360^\circ$.

$\angle ABD + 125^\circ + 119^\circ = 360^\circ$

$\angle ABD = 360^\circ - 125^\circ - 119^\circ = 116^\circ$

$\boxed{\angle ABD = 116^\circ}$

(c) Solve for $\angle z$:

• The given angles are $75^\circ, 48^\circ,$ and $87^\circ$.
• The sum of angles around a point is $360^\circ$.

$\angle z + 75^\circ + 48^\circ + 87^\circ = 360^\circ$

$\angle z = 360^\circ - 75^\circ - 48^\circ - 87^\circ = 150^\circ$

$\boxed{\angle z = 150^\circ}$

(d) Solve for $\angle EBC$:

• At point $B$, the given angles are $135^\circ, 85^\circ,$ and $110^\circ$.
• The sum of angles around a point is $360^\circ$.

$\angle EBC + 135^\circ + 85^\circ + 110^\circ = 360^\circ$

$\angle EBC = 360^\circ - 135^\circ - 85^\circ - 110^\circ = 30^\circ$

$\boxed{\angle EBC = 30^\circ}$

Let me know if you have any questions or need detailed explanations!

Related Questions:

1. Why does the sum of angles around a point always equal $360^\circ$?
2. How can complementary and supplementary angles help in solving problems like this?
3. What are other situations where angles around a point are useful in geometry?
4. How can the properties of adjacent angles or vertical angles help simplify calculations?
5. How would these solutions differ if more complex figures like polygons were involved?

Tip:

Always label and organize known and unknown angles to make it easier to track your calculations.