Question

the two triangles below are similar.
also, $m\angle h=20^\circ$ and $m\angle i=90^\circ$ as shown below.
find $m\angle x$, $m\angle y$, and $m\angle z$.
assume the triangles are accurately drawn.
$m\angle x = \square^\circ$
$m\angle y = \square^\circ$
$m\angle z = \square^\circ$

Explanation:

Step1: Find ∠G in ΔGHI

Sum of angles in a triangle is $180^\circ$.
$m\angle G = 180^\circ - m\angle H - m\angle I = 180^\circ - 20^\circ - 90^\circ = 70^\circ$

Step2: Match similar triangle angles

Similar triangles have congruent corresponding angles. From the diagram:
$\angle X \cong \angle H$, $\angle Y \cong \angle I$, $\angle Z \cong \angle G$

Step3: Assign angle measures

$m\angle X = m\angle H = 20^\circ$
$m\angle Y = m\angle I = 90^\circ$
$m\angle Z = m\angle G = 70^\circ$

Answer:

$m\angle X = 20^\circ$
$m\angle Y = 90^\circ$
$m\angle Z = 70^\circ$