Question

marco claims that it is possible for a triangle to have two obtuse angles. is he correct? explain.

Explanation:

Step1: Recall the sum of interior angles of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Analyze the property of an obtuse angle

An obtuse angle is an angle greater than \(90^{\circ}\).

Step3: Suppose there are two obtuse angles in a triangle

Let the two obtuse angles be \(\alpha\) and \(\beta\), where \(\alpha> 90^{\circ}\) and \(\beta>90^{\circ}\). Then \(\alpha+\beta>180^{\circ}\).

Step4: Consider the third angle

Let the third angle be \(\gamma\). Since \(\alpha+\beta+\gamma = 180^{\circ}\), if \(\alpha+\beta>180^{\circ}\), then \(\gamma<0^{\circ}\), which is impossible for an angle of a triangle.

Answer:

Marco is not correct. Because the sum of the interior angles of a triangle is \(180^{\circ}\), if there were two obtuse angles (each greater than \(90^{\circ}\)), their sum would exceed \(180^{\circ}\), leaving a negative value for the third - angle, which is not possible for a triangle's interior angle.