Question

17 part a - create an equation and solve for x: 149° 13x + 5° x = part b - find the measure of the unknown angle: unknown angle = degrees.

Explanation:

Step1: Use the linear - pair property

Since the two angles \(149^{\circ}\) and \((13x + 5)^{\circ}\) form a linear pair, their sum is \(180^{\circ}\). So the equation is \(149+(13x + 5)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(149+13x + 5=13x+(149 + 5)=13x+154\). So the equation becomes \(13x+154 = 180\).

Step3: Solve for \(x\)

Subtract \(154\) from both sides: \(13x+154-154=180 - 154\), which gives \(13x=26\). Then divide both sides by \(13\): \(x=\frac{26}{13}=2\).

Step4: Find the measure of the unknown angle

Substitute \(x = 2\) into \(13x + 5\). We get \(13\times2+5=26 + 5=31\).

Answer:

\(x = 2\)
Unknown angle \(=31\) degrees.