Determine the measure of this interior angle we have looks like an obtuse triangle that has 90° on it and on the other side 45° what is the measure of the interior angle?

Answer 1

In a triangle, the sum of the interior angles is always 180 degrees. If you have a triangle with one angle measuring 90 degrees (a right angle) and another measuring 45 degrees, you can find the measure of the third angle by using the following formula:

\[ \text{Measure of the third angle} = 180^\circ - (\text{angle 1} + \text{angle 2}) \]

Substituting the known values:

\[ \text{Measure of the third angle} = 180^\circ - (90^\circ + 45^\circ) \]

\[ \text{Measure of the third angle} = 180^\circ - 135^\circ \]

\[ \text{Measure of the third angle} = 45^\circ \]

So the measure of the interior angle is 45 degrees. Since this is a right triangle, it is not obtuse. An obtuse angle would be greater than 90 degrees, and in the case of your triangle, all angles are either 90 or 45 degrees, which makes it a right triangle.