Answer
$H$
Work Step by Step
To figure what kind of triangle the diagram shows, we want to figure out what all the interior angles measure. We know that the sum of all the interior angles of a triangle equals $180^{\circ}$, so if we have the measure of two interior angles, we can find the measure of the third angle with the following equation:
$m \angle PUT = 180 - (m \angle PTU + m \angle TPU)$
Let's plug in what we know:
$m \angle PUT = 180 - (42 + 45)$
Evaluate what is in parentheses first, according to order of operations:
$m \angle PUT = 180 - (87)$
Subtract to solve:
$m \angle PUT = 93$
This angle is obtuse because it is greater than $90^{\circ}$. If one angle in a triangle is an obtuse angle, then the triangle is an obtuse triangle.
