# 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°.

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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