Question

find the measure of each angle.
(15x - 2)°
(7x + 4)°
m∠bac =
°
m∠cad =
°

Explanation:

Step1: Set up the equation

Since $\angle BAC$ and $\angle CAD$ are complementary (the right - angle symbol indicates $\angle BAD = 90^{\circ}$), we have $(15x - 2)+(7x + 4)=90$.

Step2: Combine like terms

Combine the $x$ terms and the constant terms: $15x+7x-2 + 4=90$, which simplifies to $22x+2 = 90$.

Step3: Solve for $x$

Subtract 2 from both sides: $22x=90 - 2=88$. Then divide both sides by 22, so $x=\frac{88}{22}=4$.

Step4: Find $m\angle BAC$

Substitute $x = 4$ into the expression for $\angle BAC$: $m\angle BAC=15x-2=15\times4-2=60 - 2=58^{\circ}$.

Step5: Find $m\angle CAD$

Substitute $x = 4$ into the expression for $\angle CAD$: $m\angle CAD=7x + 4=7\times4+4=28+4=32^{\circ}$.

Answer:

$m\angle BAC = 58$
$m\angle CAD = 32$