Question

what is the greatest number of acute angles that a triangle can contain?
a. 0
b. 1
c. 2
d. 3

Explanation:

Step1: Recall triangle angle sum

A triangle's interior angles sum to \(180^\circ\). An acute angle is less than \(90^\circ\).

Step2: Analyze maximum acute angles

If we have 3 acute angles, say each is \(60^\circ\) (since \(60^\circ<90^\circ\) and \(3\times60^\circ = 180^\circ\)), this works (equilateral triangle). For more than 3, but a triangle has 3 angles. Checking other options: 0 or 1 acute angles would mean at least 2 non - acute (right or obtuse), but two right angles (\(90^\circ+90^\circ = 180^\circ\)) can't form a triangle (needs 3 angles), and two obtuse angles would sum to more than \(180^\circ\). So 3 is possible.

Answer:

D. 3