Question

a triangle can have at most ______ right angle.
○ 4
○ 1
○ 0
○ 2

Explanation:

Step1: Recall triangle angle sum property

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

Step2: Analyze right angle ( \(90^\circ\) ) in a triangle

Let's assume a triangle has \(n\) right angles. Each right angle is \(90^\circ\), so the sum of \(n\) right angles is \(90n^\circ\). The remaining \((3 - n)\) angles must be non - negative (since angle measure is non - negative). If \(n = 2\), then the sum of two right angles is \(90\times2=180^\circ\), and the third angle would be \(180 - 180 = 0^\circ\), which is not a valid triangle angle. If \(n = 1\), the sum of the other two angles is \(180 - 90=90^\circ\), which is valid as long as each of the other two angles is positive. If \(n\geq2\), we get a non - valid triangle as shown above. Also, a triangle has 3 angles, so \(n\) can't be 4. And a triangle can have 1 right angle (like a right - angled triangle), so a triangle can have at most 1 right angle.

Answer:

1 (corresponding to the option "1")