Question

which is the sum of the 2 smaller angles in a right - triangle?
a. 30 degrees
b. 45 degrees
c. 90 degrees
d. 180 degrees
e. 360 degrees

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180 degrees. In a right - triangle, one angle is 90 degrees. Let the two non - right angles be \(x\) and \(y\). Then \(x + y+90^{\circ}=180^{\circ}\), so \(x + y = 90^{\circ}\).

Step2: Analyze non - right angles

The non - right angles in a right - triangle are acute (less than 90 degrees). The most common case for the two non - right angles in a right - triangle is when they are equal, i.e., \(x=y = 45^{\circ}\) (isosceles right - triangle). In general, the non - right angles are acute and their sum is 90 degrees. The smallest non - zero values for the non - right angles occur when the triangle is non - isosceles right - triangle, but the non - right angles are still acute. The smallest non - zero acute angle among the non - right angles in a right - triangle can be close to 0 but in the case of a non - degenerate triangle, the most common and well - known non - right angle value in a right - triangle is 45 degrees when it is an isosceles right - triangle.

Answer:

B. 45 degrees