Question

1. question: two adjacent angles sum to 90 degrees. if the angle measures are 11x - 20 and x + 2, solve for x.

a. x = 9
b. x = 10
c. x = 7.5
d. x = 12

Explanation:

Step1: Set up the equation

Since the two adjacent angles sum to \(90^{\circ}\), we have \((11x - 20)+(x + 2)=90\).

Step2: Simplify the left - hand side

Combine like terms: \(11x+x-20 + 2=90\), which simplifies to \(12x-18 = 90\).

Step3: Isolate the term with \(x\)

Add \(18\) to both sides: \(12x-18+18=90 + 18\), so \(12x=108\).

Step4: Solve for \(x\)

Divide both sides by \(12\): \(x=\frac{108}{12}\).

Answer:

\(x = 9\), so the answer is A.