Question

#15: m∠cab =________*
your answer
#16: m∠cad =________*
your answer

Explanation:

Step1: Assume angles are supplementary

If $\angle CAB$ and $\angle CAD$ are supplementary, then $\angle CAB+\angle CAD = 180^{\circ}$. So, $(7x + 1)+(5x+3)=180$.

Step2: Combine like - terms

$7x+5x + 1+3=180$, which simplifies to $12x+4 = 180$.

Step3: Solve for x

Subtract 4 from both sides: $12x=180 - 4=176$. Then $x=\frac{176}{12}=\frac{44}{3}$.

Step4: Find $\angle CAB$

Substitute $x = \frac{44}{3}$ into the expression for $\angle CAB$: $\angle CAB=7x + 1=7\times\frac{44}{3}+1=\frac{308}{3}+1=\frac{308 + 3}{3}=\frac{311}{3}\approx103.67^{\circ}$.

Step5: Find $\angle CAD$

Substitute $x=\frac{44}{3}$ into the expression for $\angle CAD$: $\angle CAD=5x + 3=5\times\frac{44}{3}+3=\frac{220}{3}+3=\frac{220+9}{3}=\frac{229}{3}\approx76.33^{\circ}$.

Answer:

#15: $\frac{311}{3}$
#16: $\frac{229}{3}$