Problem 75 - Introductory Algebra for College Students

Question

Can a triangle contain two \(90^{\circ}\) angles? Explain your answer.

Step-by-Step Solution

Answer

No, a triangle cannot contain two \(90^{\circ}\) angles because the total sum of a triangle's internal angles must equal \(180^{\circ}\).

Step 1: Recall the properties of a triangle

One of the fundamental properties of a triangle is that the sum of its internal angles is always equal to \(180^{\circ}\).

Step 2: Consider the possibility of two right angles

If a triangle had two angles that were each \(90^{\circ}\), the total for these two angles alone would already be \(180^{\circ}\), leaving no space for the third angle.

Step 3: Conclude the analysis

Therefore, it is impossible for a triangle to contain two \(90^{\circ}\) angles, as it would exceed the total internal angle sum of \(180^{\circ}\) of a triangle.