Question

one angle of a triangle is obtuse. the sum of the measures of the other angles must be
less than 90 degrees
more than 90 degrees
equal to 90 degrees

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Define obtuse angle

An obtuse angle is greater than \(90^\circ\) and less than \(180^\circ\). Let the obtuse angle be \(O\), so \(90^\circ < O < 180^\circ\). Let the other two angles be \(A\) and \(B\).

Step3: Find sum of \(A + B\)

We know \(A + B + O = 180^\circ\), so \(A + B = 180^\circ - O\). Since \(O>90^\circ\), subtracting a number greater than \(90^\circ\) from \(180^\circ\) gives \(A + B<180^\circ - 90^\circ = 90^\circ\).

Answer:

less than 90 degrees