Question

for the following intersection, the measurements of the indicated angles are represented by the expressions $mangle c=(-9x + 127)^{circ}$ and $mangle d=(-9x + 143)^{circ}$. what are the numerical angle measurements of $angle c$ and $angle d$?

Explanation:

Step1: Set up equation

Since $\angle c$ and $\angle d$ are complementary (sum to 90°), we have $(-9x + 127)+(-9x + 143)=90$.

Step2: Combine like - terms

$-9x-9x+127 + 143=90$, which simplifies to $-18x+270 = 90$.

Step3: Isolate the variable term

Subtract 270 from both sides: $-18x=90 - 270=-180$.

Step4: Solve for x

Divide both sides by - 18: $x=\frac{-180}{-18}=10$.

Step5: Find measure of $\angle c$

Substitute $x = 10$ into the expression for $m\angle c$: $m\angle c=-9(10)+127=-90 + 127 = 37^{\circ}$.

Step6: Find measure of $\angle d$

Substitute $x = 10$ into the expression for $m\angle d$: $m\angle d=-9(10)+143=-90 + 143 = 53^{\circ}$.

Answer:

$m\angle c = 37^{\circ}$, $m\angle d = 53^{\circ}$