Question

∠ads and ∠bct are complementary. if m∠ads = 3z - 1 and m∠bct = z + 7, find m∠ads. after you enter your answer press go. m∠ads =

Explanation:

Step1: Use complementary - angle property

Since $\angle ADS$ and $\angle BCT$ are complementary, $m\angle ADS + m\angle BCT=90^{\circ}$.
So, $(3z - 1)+(z + 7)=90$.

Step2: Simplify the left - hand side

Combine like terms: $3z-1+z + 7=(3z+z)+(-1 + 7)=4z + 6$.
The equation becomes $4z+6 = 90$.

Step3: Solve for $z$

Subtract 6 from both sides: $4z+6-6=90 - 6$, which gives $4z=84$.
Divide both sides by 4: $z=\frac{84}{4}=21$.

Step4: Find $m\angle ADS$

Substitute $z = 21$ into the expression for $m\angle ADS$: $m\angle ADS=3z-1$.
$m\angle ADS=3\times21-1=63 - 1=62$.

Answer:

$62$