Question

extra credit points will be awarded after homework closure deadline. select all true statements about triangles: the exterior angle of a triangle is equal to the sum of the two adjacent interior angles a right triangle may contain an acute angle. a triangle cannot contain more than one acute angle. interior angles sum to 180° exterior angles sum to 360° exterior angles sum to 180° the sum of an interior angle and its matching exterior angle is 180° one side of a triangle cannot be longer than the sum of the other two sides.

Explanation:

Step1: Recall exterior - angle property

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles, not adjacent ones. So the statement "The exterior angle of a triangle is equal to the sum of the two adjacent interior angles" is false.

Step2: Analyze right - triangle angles

A right triangle has one right angle ($90^{\circ}$) and two acute angles (angles less than $90^{\circ}$). So the statement "A right triangle MAY contain an acute angle" is true.

Step3: Consider acute angles in a triangle

A triangle can have three acute angles (an acute - angled triangle), so the statement "A triangle CANNOT contain more than one acute angle" is false.

Step4: Recall interior - angle sum

The sum of the interior angles of a triangle is always $180^{\circ}$. So the statement "Interior angles sum to $180^{\circ}$" is true.

Step5: Recall exterior - angle sum

The sum of the exterior angles of any polygon, including a triangle, is $360^{\circ}$. So the statement "Exterior angles sum to $360^{\circ}$" is true and "Exterior angles sum to $180^{\circ}$" is false.

Step6: Recall interior - exterior angle relation

The sum of an interior angle and its corresponding exterior angle of a triangle is $180^{\circ}$. So the statement "The sum of an interior angle and its matching exterior angle is $180^{\circ}$" is true.

Step7: Recall triangle side - length property

By the triangle inequality theorem, one side of a triangle CANNOT be longer than the sum of the other two sides. So the statement "One side of a triangle CANNOT be longer than the sum of the other two sides" is true.

Answer:

A right triangle MAY contain an acute angle.
Interior angles sum to $180^{\circ}$.
Exterior angles sum to $360^{\circ}$.
The sum of an interior angle and its matching exterior angle is $180^{\circ}$.
One side of a triangle CANNOT be longer than the sum of the other two sides.