Question

the figure shows adjacent angles bac and cad. given: m∠bad = 134°, m∠bac=(2x + 3)°, m∠cad=(4x - 1)°. part a: using the angle addition postulate, write and solve an equation for x. show all your work (6 points). part b: find the m∠cad. show all your work (4 points).

Explanation:

Step1: Apply angle - addition postulate

Since $\angle BAD=\angle BAC+\angle CAD$, we have the equation $(2x + 3)+(4x-1)=134$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $2x+4x+3 - 1=134$, which simplifies to $6x+2 = 134$.

Step3: Isolate the variable term

Subtract 2 from both sides of the equation: $6x+2-2=134 - 2$, resulting in $6x=132$.

Step4: Solve for $x$

Divide both sides by 6: $\frac{6x}{6}=\frac{132}{6}$, so $x = 22$.

Step5: Find $m\angle CAD$

Substitute $x = 22$ into the expression for $m\angle CAD$. We know that $m\angle CAD=(4x-1)^{\circ}$.
So $m\angle CAD=4\times22-1$.
$m\angle CAD = 88 - 1=87^{\circ}$.

Answer:

Part A: $x = 22$
Part B: $m\angle CAD=87^{\circ}$