Question

1. if one of the angles of a right triangle is 30 degrees, what are the other two angles? (a) 30 degrees, 120 degrees (b) 60 degrees, 45 degrees (c) 60 degrees, 90 degrees (d) 45 degrees, 90 degrees

Explanation:

Step1: Recall right - triangle property

A right - triangle has one angle equal to 90 degrees.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180 degrees. Let the three angles of the triangle be \(A\), \(B\), and \(C\). We know \(A = 30^{\circ}\) and one angle is a right - angle, so \(B=90^{\circ}\). Then, using \(A + B+C=180^{\circ}\), we substitute the known values: \(30^{\circ}+90^{\circ}+C = 180^{\circ}\). Solving for \(C\), we get \(C=180^{\circ}-(30^{\circ}+90^{\circ})=60^{\circ}\).

Answer:

C. 60 degrees, 90 degrees