Question

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

Explanation:

Step1: Set up equation

Since $\angle BAC$ and $\angle CAD$ are complementary (the right - angle symbol indicates their sum is 90°), we have $(15x - 2)+(7x + 4)=90$.

Step2: Combine like terms

$15x+7x-2 + 4=90$, which simplifies to $22x+2 = 90$.

Step3: Isolate the variable term

Subtract 2 from both sides: $22x=90 - 2$, so $22x=88$.

Step4: Solve for x

Divide both sides by 22: $x=\frac{88}{22}=4$.

Step5: Find $m\angle BAC$

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

Step6: Find $m\angle CAD$

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

Answer:

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