Question

c. can a triangle be constructed with two obtuse angles?
a. yes, it is possible. the third angle will equal the difference between 180 and the sum of the two given angles
b. no, it is not possible. a triangle can only have at most one obtuse angle
c. no, it is not possible. at least one side needs to be known in order to construct a triangle with two obtuse angles
d. no, it is not possible. all three angles must be known in order to construct a triangle with two obtuse angles

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is always 180 degrees. An obtuse angle is an angle greater than 90 degrees.

Step2: Analyze the sum of two obtuse angles

If we have two obtuse angles, say $\alpha>90^{\circ}$ and $\beta > 90^{\circ}$, then $\alpha+\beta>180^{\circ}$. So, it is not possible to have a third - angle $\gamma$ such that $\alpha+\beta+\gamma = 180^{\circ}$. A triangle can only have at most one obtuse angle.

Answer:

B. No, it is not possible. A triangle can only have at most one obtuse angle.