Question

if m∠acb = m∠acd = 67°, ab = s + 48, and ad = 4s, what is the value of s?

Explanation:

Step1: Identify congruent triangles

Since $\angle ACB=\angle ACD = 67^{\circ}$, $\angle B=\angle D = 90^{\circ}$ and $AC$ is common to both $\triangle ABC$ and $\triangle ADC$, by the Angle - Angle - Side (AAS) congruence criterion, $\triangle ABC\cong\triangle ADC$.

Step2: Set up equation from congruent - side property

For congruent triangles, corresponding sides are equal. So $AB = AD$. Given $AB=s + 48$ and $AD = 4s$, we set up the equation $s + 48=4s$.

Step3: Solve the equation for s

Subtract $s$ from both sides: $48=4s - s$.
Simplify the right - hand side: $48 = 3s$.
Divide both sides by 3: $s=\frac{48}{3}=16$.

Answer:

$16$