In the figure above, if the measure of ∠1 is not equal to the measure of ∠4, then the cosine of which of the following is equal to the sine of ∠1 ?

In this scenario, let's break down the problem step by step to determine which angle's cosine is equal to the sine of ∠1.

1. Break Down the Problem

• We need to find an angle $\theta$ such that $\cos(\theta) = \sin(\angle 1)$.
• We know from trigonometric identity that $\sin(x) = \cos(90^\circ - x)$.

2. Relevant Concepts

Using the identity mentioned, we have: $\sin(\angle 1) = \cos(90^\circ - \angle 1)$

3. Analysis and Detail

From the above identity, we can directly conclude:

• The cosine of the angle $(90^\circ - \angle 1)$ is equal to the sine of $\angle 1$.

4. Verify and Summarize

Since $\cos(90^\circ - \angle 1) = \sin(\angle 1)$, we have verified that the trigonometric relationships hold true.

Final Answer

Thus, the cosine of $(90^\circ - \angle 1)$ is equal to the sine of $\angle 1$.