Question

use the angle addition postulate to find the value of x, then find the measure of the indicated angle. find x, then m∠nbs. m∠nbr = 17x + 8

Explanation:

Step1: Apply Angle - Addition Postulate

According to the Angle - Addition Postulate, \(m\angle NBS=m\angle NBR + m\angle RBS\). So, \(17x + 8=(12x+4)+42\).

Step2: Simplify the equation

First, combine like - terms on the right - hand side: \(17x + 8=12x+46\). Then, subtract \(12x\) from both sides: \(17x-12x+8=12x - 12x+46\), which gives \(5x+8 = 46\). Next, subtract 8 from both sides: \(5x+8 - 8=46 - 8\), so \(5x=38\). Finally, divide both sides by 5: \(x=\frac{38}{5}=7.6\).

Step3: Find the measure of \(\angle NBS\)

Substitute \(x = 7.6\) into the expression for \(m\angle NBS\): \(m\angle NBS=17x + 8\). \(m\angle NBS=17\times7.6+8\). First, calculate \(17\times7.6 = 129.2\). Then, \(129.2+8=137.2\).

Answer:

\(x = 7.6\)
\(m\angle NBS=137.2\) degrees