Question

which set of angles can form a triangle? 1 acute, 1 right, and 1 obtuse; 2 acute and 1 right; 1 acute and 2 right; 1 acute and 2 obtuse

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is $180^\circ$.

Step2: Analyze Option 1

1 acute ($<90^\circ$), 1 right ($=90^\circ$), 1 obtuse ($>90^\circ$): Sum $>90+90=180^\circ$, invalid.

Step3: Analyze Option 2

2 acute, 1 right: Sum $=a+b+90$, where $a,b<90$. $a+b=90$, total $180^\circ$, valid.

Step4: Analyze Option 3

1 acute, 2 right: Sum $>90+90=180^\circ$, invalid.

Step5: Analyze Option 4

1 acute, 2 obtuse: Sum $>90+90=180^\circ$, invalid.

Answer:

2 acute and 1 right