Question

which dimensions cannot create a triangle? three angles measuring 40°,70°, and 65° three sides measuring 6 cm,8 cm, and 10 cm three angles measuring 10°,25°, and 145° three sides measuring 9 m,15 m, and 9 m

Explanation:

Step1: Check angle sum for triangle

The sum of interior angles of a triangle is \(180^{\circ}\).
For the first set of angles: \(40^{\circ}+70^{\circ}+65^{\circ}=175^{\circ}
eq180^{\circ}\).
For the second set of angles: \(10^{\circ}+25^{\circ}+145^{\circ}=180^{\circ}\).

Step2: Check triangle inequality for side lengths

The triangle inequality states that for three side lengths \(a\), \(b\), \(c\) (\(a\leq b\leq c\)), \(a + b>c\).
For \(6\), \(8\), \(10\): \(6 + 8>10\), \(6+10>8\), \(8 + 10>6\).
For \(9\), \(9\), \(15\): \(9+9 = 18>15\), \(9+15>9\), \(9+15>9\).

Answer:

three angles measuring \(40^{\circ}\), \(70^{\circ}\), and \(65^{\circ}\)