Question

a ramp forms the angles shown to the right. what are the values of a and b? the value of a is □

Explanation:

Step1: Use angle - sum property of a triangle

In the right - triangle, one angle is 90° and another is 76°. Let the third angle be \(x\). Then \(x + 90^{\circ}+76^{\circ}=180^{\circ}\) (since the sum of angles in a triangle is 180°). So \(x=180^{\circ}-(90^{\circ} + 76^{\circ})=14^{\circ}\).

Step2: Relate angles \(a\) and \(x\)

Angle \(a\) and \(x\) are vertical angles. Vertical angles are equal. So \(a = 14^{\circ}\).

Step3: Relate angles \(b\) and \(x\)

Angle \(b\) and \(x\) are complementary angles (because the ramp and the vertical line form a right - angle). So \(b=90^{\circ}-x\). Substituting \(x = 14^{\circ}\), we get \(b = 76^{\circ}\).

Answer:

\(a = 14^{\circ}\), \(b = 76^{\circ}\)