Question

question 4 (2 points)
given: $mangle a=(4x - 2)^{circ}$ and $mangle b=(11x + 17)^{circ}$
a) find x if the angles are complementary: x =

b) find x if the angles are supplementary: x =

blank 1:

blank 2:

Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90°. So, $(4x - 2)+(11x + 17)=90$.

Step2: Combine like - terms

$4x+11x-2 + 17=90$, which simplifies to $15x+15 = 90$.

Step3: Isolate the variable term

Subtract 15 from both sides: $15x=90 - 15$, so $15x=75$.

Step4: Solve for x

Divide both sides by 15: $x=\frac{75}{15}=5$.

Step5: Recall supplementary - angle property

Supplementary angles sum to 180°. So, $(4x - 2)+(11x + 17)=180$.

Step6: Combine like - terms

$4x+11x-2 + 17=180$, which simplifies to $15x+15 = 180$.

Step7: Isolate the variable term

Subtract 15 from both sides: $15x=180 - 15$, so $15x=165$.

Step8: Solve for x

Divide both sides by 15: $x=\frac{165}{15}=11$.

Answer:

Blank 1: 5
Blank 2: 11