Question

△qrs ~ △cdb. what is m∠d?
m∠d = \square°

Explanation:

Step1: Recall Similar Triangles Property

Similar triangles have corresponding angles equal. So, $\triangle QRS \sim \triangle CDB$ implies $\angle R = \angle C$, $\angle Q = \angle D$, $\angle S = \angle B$.

Step2: Use Triangle Angle Sum

In a triangle, the sum of angles is $180^\circ$. For $\triangle QRS$, we know $\angle R = 51^\circ$ and for $\triangle CDB$, $\angle B = 87^\circ$ (which corresponds to $\angle S$). Let $\angle D = \angle Q = x$. Then in $\triangle QRS$ (or $\triangle CDB$), $51^\circ + x + 87^\circ = 180^\circ$.

Step3: Solve for x

Simplify the equation: $x + 138^\circ = 180^\circ$. Subtract $138^\circ$ from both sides: $x = 180^\circ - 138^\circ = 42^\circ$.

Answer:

$42$