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Chapter 13: Problem 1

Which of the following could be the degree measures of two angles in a right triangle? Indicate all such angles. A. \(20^{\circ}\) and \(70^{\circ}\) B. \(30^{\circ}\) and \(60^{\circ}\) C. \(45^{\circ}\) and \(45^{\circ}\) D. \(55^{\circ}\) and \(55^{\circ}\) E. \(75^{\circ}\) and \(75^{\circ}\)

Short Answer

Expert verified
The degree measures of two angles in a right triangle could be (A) \(20^{\circ}\) and \(70^{\circ}\), (B) \(30^{\circ}\) and \(60^{\circ}\), and (C) \(45^{\circ}\) and \(45^{\circ}\).

Step by step solution

01

Checking through the option

Start with option A, adding \(20^{\circ}\) and \(70^{\circ}\) gives us \(90^{\circ}\). So, this pair could be the angles in a right triangle.
02

Comparing with the sum required

For option B, the sum of \(30^{\circ}\) and \(60^{\circ}\) is \(90^{\circ}\), again meeting the requirement for a pair of angles in a right triangle.
03

Further check through the options

For options C, D, and E, the sum of each pair of angles is \(90^{\circ}\), \(110^{\circ}\), and \(150^{\circ}\) respectively. Only option C could therefore be angles in a right triangle.

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