Question

6.
40°
8r + 2°
16r - 6°
r = ____

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we set up the equation \(40+(8r + 2)+(16r-6)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(40 + 8r+2+16r - 6=(8r+16r)+(40 + 2-6)=24r + 36\). So the equation becomes \(24r+36 = 180\).

Step3: Isolate the variable term

Subtract 36 from both sides of the equation: \(24r+36-36=180 - 36\), which gives \(24r=144\).

Step4: Solve for r

Divide both sides of the equation by 24: \(\frac{24r}{24}=\frac{144}{24}\), so \(r = 6\).

Answer:

6