Question

In a right triangle, the acute angles have the relationship sin(x + 12º) = cos cos(18" + 2x).

What is the value of x?

What is the measure of the smaller angle?

Use 2 sentences to explain how you arrived at your answers. In a 6th graders response (2 points)

Answer 1

To find the value of \( x \), we can use the fact that \( \sin(x + 12^\circ) = \cos(18^\circ + 2x) \) means that \( x + 12^\circ + (18^\circ + 2x) = 90^\circ \). Solving this gives us \( 3x + 30^\circ = 90^\circ \), which simplifies to \( 3x = 60^\circ \) and \( x = 20^\circ \); thus, the smaller angle in the triangle is \( x = 20^\circ \).