SAT Question 14e7c1f4: Right Triangles And Trigonometry answer and explanation with Desmos solution

Choice A is correct. It's given that for two acute angles, $\angle Q$ and $\angle R$, $\cos (Q)=\sin (R)$. For two acute angles, if the sine of one angle is equal to the cosine of the other angle, the angles are complementary. It follows that $\angle Q$ and $\angle R$ are complementary. That is, the sum of the measures of the angles is $90$ degrees. It's given that the measure of $\angle Q$ is $x+61$ degrees and the measure of $\angle R$ is $4x+4$ degrees. It follows that $(x+61)+(4x+4)=90$. By combining like terms, this equation can be rewritten as $5x+65=90$. Subtracting $65$ from each side of this equation yields $5x=25$. Dividing each side of this equation by $5$ yields $x=5$.