Question

question 1 (multiple choice worth 1 points) (05.02r mc) if sin∠m = cos∠n and m∠n = 30°, what is the measure of ∠m? 150° 90° 60° 30°

Explanation:

Step1: Recall co-function identity

We know the co - function identity: $\sin\theta=\cos(90^{\circ}-\theta)$ and also if $\sin A = \cos B$, then $A + B=90^{\circ}$ (when $A$ and $B$ are acute angles, which is a common case in such problems). Given that $\sin\angle M=\cos\angle N$ and $m\angle N = 30^{\circ}$.

Step2: Substitute the value of $\angle N$

Using the relationship $\sin\angle M=\cos\angle N$ and the co - function identity, we can say that $\angle M+ \angle N=90^{\circ}$ (because $\sin x=\cos(90 - x)$ implies that if $\sin\angle M=\cos\angle N$, then $\angle M = 90^{\circ}-\angle N$ when we consider the acute angle case). Substitute $\angle N = 30^{\circ}$ into the equation $\angle M=90^{\circ}-\angle N$.
$\angle M=90^{\circ}- 30^{\circ}=60^{\circ}$

Answer:

$60^{\circ}$ (The option corresponding to $60^{\circ}$)