Question

determining triangle existence using angle measure
under which angle conditions could a triangle exist? choose three correct answers.
2 acute angles, 1 obtuse
angle
1 acute angle; 2 obtuse
angles
1 acute angle, 1 right
angle, 1 obtuse angle
3 acute angles
2 acute angles; 1 right
angle

Explanation:

Step1: Recall the sum of triangle angles

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

Step2: Analyze each option

• Option 1: 2 acute angles, 1 obtuse angle

Let the acute angles be \(a\) and \(b\) (\(0^{\circ}

• Option 2: 1 acute angle, 2 obtuse angles

Let the acute angle be \(x\) (\(0^{\circ}90^{\circ}+90^{\circ}+0^{\circ}=180^{\circ}\), so this is not possible.

• Option 3: 1 acute angle, 1 right angle, 1 obtuse angle

Let the acute angle be \(m\) (\(0^{\circ}90^{\circ}+90^{\circ}+0^{\circ}=180^{\circ}\), so this is not possible.

• Option 4: 3 acute angles

Let the angles be \(q\), \(r\), \(s\) (\(0^{\circ}

• Option 5: 2 acute angles, 1 right angle

Let the acute angles be \(u\) and \(v\) (\(0^{\circ}

Answer:

2 acute angles, 1 obtuse angle; 3 acute angles; 2 acute angles, 1 right angle.