One angle of a triangle is obtuse. The sum of the measures of the other angles must be
Less than 90 degrees. 
Equal to 90 degrees. 
More than 90 degrees
None of the above

Solution:

An obtuse angle is an angle greater than 90°.

An obtuse triangle is a triangle in which one of the interior angles is greater than 90°.

It has one of its vertex angles as obtuse and other angles as acute angles.

When one angle measures more than 90°, the sum of the other two angles is less than 90°.

if one angle of a triangle is obtuse the sum of the measures of the other angles < 90 degrees. 

Let us consider an obtuse triangle ABC as shown in the figure,

Some of the properties of the obtuse triangle are:

  • The longest side of a triangle is the side opposite to the obtuse angle

In triangle ABC, the obtuse angle is 110°and the longest side is AC.

  • A triangle can only have one obtuse angle

Triangle ABC contain only one obtuse angle i.e.110°

  • The sum of the other two angles in an obtuse triangle is always smaller than 90°

In triangle ABC, sum of angles 40° + 30°= 70° < 90° 

Therefore, the sum of the other two angles will always be less than 90°.

One angle of a triangle is obtuse. The sum of the measures of the other angles must be

Summary:

One angle of a triangle is obtuse. The sum of the measures of the other angles must be less than 90°.

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