Question

one of the angles of $\triangle def$ has a measure of $47^\circ$. one of the angles of $\triangle pqr$ has a measure of $86^\circ$. if $\triangle def$ and $\triangle pqr$ are similar, what is the measure of the largest angle of $\triangle def$?

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles of a triangle is $180^\circ$.

Step2: Find missing angle in similar triangles

We know two angles across the similar triangles: $47^\circ$ and $86^\circ$. Calculate the third angle:
$180^\circ - 47^\circ - 86^\circ = 47^\circ$

Step3: Identify largest angle

The angles of $\triangle DEF$ are $47^\circ$, $47^\circ$, and $86^\circ$.

Answer:

$86^\circ$