Question

question 7 of 10
what is the greatest number of obtuse angles that a right triangle can contain?
a. 0
b. 1
c. 2
d. 3

Explanation:

Step1: Recall the angle sum property of a triangle

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

Step2: Recall the definitions of right - angled and obtuse angles

A right - angled triangle has one angle equal to \(90^{\circ}\). An obtuse angle is an angle greater than \(90^{\circ}\) but less than \(180^{\circ}\).

Step3: Analyze the possibility of having obtuse angles in a right - angled triangle

Let the angles of the triangle be \(A\), \(B\), and \(C\) where \(A = 90^{\circ}\). If there was an obtuse angle \(B>90^{\circ}\), then \(A + B>180^{\circ}\). But since \(A + B + C=180^{\circ}\), having two or more obtuse angles (along with a right angle) would violate the angle - sum property of a triangle. Also, if we consider one obtuse angle and one right angle: \(90^{\circ}+\text{obtuse angle}(>90^{\circ})+\text{third angle}>180^{\circ}\).

Answer:

A. 0