Question

1. an isosceles triangle has one angle that measures 98°. find the measures of the other two angles and classify the triangle as acute, right, or obtuse.

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. In an isosceles triangle, two angles are equal.

Step2: Determine if the 98° angle is the non - equal angle

Since 98°>90°, it must be the non - equal angle. Let the measure of each of the equal angles be $x$. Then, using the angle - sum property of a triangle, we have the equation $x + x+98^{\circ}=180^{\circ}$.

Step3: Solve the equation for $x$

Combining like terms gives $2x+98^{\circ}=180^{\circ}$. Subtract 98° from both sides: $2x=180^{\circ}-98^{\circ}=82^{\circ}$. Divide both sides by 2: $x = 41^{\circ}$.

Step4: Classify the triangle

Since one of the angles (98°) is greater than 90°, the triangle is an obtuse triangle.

Answer:

The measures of the other two angles are 41° and 41°. The triangle is an obtuse triangle.