Question

1. 28° 15° 85° $x^\circ$ $y^\circ$ $z^\circ$

Explanation:

Step1: Calculate $\angle x$ (triangle sum)

The sum of angles in a triangle is $180^\circ$. For the leftmost triangle:
$$x^\circ = 180^\circ - 85^\circ - 28^\circ$$
$$x^\circ = 67^\circ$$

Step2: Find adjacent angle to $x$

$\angle x$ and its supplementary angle form a straight line:
$$180^\circ - 67^\circ = 113^\circ$$

Step3: Calculate $\angle y$ (triangle sum)

For the middle triangle, use angle sum:
$$y^\circ = 180^\circ - 113^\circ - 15^\circ$$
$$y^\circ = 52^\circ$$

Step4: Find adjacent angle to $y$

$\angle y$ and its supplementary angle form a straight line:
$$180^\circ - 52^\circ = 128^\circ$$

Step5: Calculate total top angle

Add the two top angles:
$$28^\circ + 15^\circ = 43^\circ$$

Step6: Calculate $\angle z$ (triangle sum)

For the largest triangle, use angle sum:
$$z^\circ = 180^\circ - 85^\circ - 43^\circ$$
$$z^\circ = 52^\circ$$

Answer:

$x = 67$, $y = 52$, $z = 52$