Question

the exterior sides of two adjacent angles make a right angle. the first angle has a measure that is 6 more than half of the second. what are the measures of both angles? after you enter your answer press go. and go

Explanation:

Step1: Set up equations

Let the second angle be \(x\). The first angle is \(\frac{x}{2}+6\). Since the sum of the two adjacent angles (whose exterior sides make a right - angle) is \(90^{\circ}\), we have the equation \((\frac{x}{2}+6)+x = 90\).

Step2: Simplify the equation

Combine like terms: \(\frac{x}{2}+x+6=90\). \(\frac{x + 2x}{2}+6 = 90\), \(\frac{3x}{2}+6=90\).
Subtract 6 from both sides: \(\frac{3x}{2}=90 - 6=84\).

Step3: Solve for \(x\)

Multiply both sides by \(\frac{2}{3}\): \(x = 84\times\frac{2}{3}=56\).

Step4: Find the first angle

Substitute \(x = 56\) into \(\frac{x}{2}+6\). \(\frac{56}{2}+6=28 + 6=34\).

Answer:

\(34\) and \(56\)