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Chapter 2: Problem 75

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

Short Answer

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

Step by step solution

01

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 \(180^{\circ}\).
02

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.
03

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.

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