What is angle S and what is angle U?

Question

asked Aug 22, 2023 16.7k views

1 Answer

Thijs Wouters · Answer 1 · 2023-08-25T21:59:34+0000

Answer:

$m\angle S=119^\circ$ ,
$m\angle U=87^\circ$

Explanation:

Since
$STUVW \sim HIJFG$ , we know that

$m\angle S=m\angle H$ and
$m\angle U=m\angle J$

since corresponding angles in similar triangles are equal in measure.

Therefore, looking at the second diagram, we see

$m\angle H=119^\circ$ and
$m\angle J=87^\circ$ .

Plugging these values into the equations we found in the first step, we get

$m\angle S=m\angle H=119^\circ$ and
$m\angle U=m\angle J=87^\circ.$

So, we have
$\boxed{m\angle S=119^\circ}$ and
$\boxed{m\angle U=87^\circ}$ .