Question

the two triangles below are similar. also, m∠z = 20° and m∠y = 120° as shown below. find m∠g, m∠h, and m∠i. assume the triangles are accurately drawn.

Explanation:

Step1: Recall property of similar triangles

Corresponding angles of similar triangles are equal.

Step2: Identify corresponding angles

Assume $\angle Z$ corresponds to $\angle I$, $\angle Y$ corresponds to $\angle H$, and the third - angles correspond. So $m\angle I = m\angle Z=20^{\circ}$ and $m\angle H = m\angle Y = 120^{\circ}$.

Step3: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle GHI$, let $m\angle G=x$. Then $x + m\angle H+m\angle I=180^{\circ}$. Substitute $m\angle H = 120^{\circ}$ and $m\angle I = 20^{\circ}$ into the equation: $x+120^{\circ}+20^{\circ}=180^{\circ}$, so $x=m\angle G=180^{\circ}-(120^{\circ} + 20^{\circ})=40^{\circ}$.

Answer:

$m\angle G = 40^{\circ}$
$m\angle H = 120^{\circ}$
$m\angle I = 20^{\circ}$