Question

the sum of the angles of a triangle is 180°. if one angle of a triangle measures x and the second angle measures (5x + 9)°, express the measure of the third angle in terms of x. simplify the expression. the measure of angle b is ( )°. (simplify your answer.)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(A=x^{\circ}\), \(B\), and \(C=(5x + 9)^{\circ}\). So, \(A + B+C=180^{\circ}\).

Step2: Substitute the known angles

Substitute \(A = x\) and \(C=(5x + 9)\) into the equation \(A + B+C=180\). We get \(x + B+(5x + 9)=180\).

Step3: Solve for \(B\)

First, combine like - terms on the left - hand side: \((x+5x)+B + 9=180\), which simplifies to \(6x+B + 9=180\). Then, isolate \(B\) by subtracting \(6x\) and \(9\) from both sides of the equation. \(B=180-(6x + 9)\). Expand the right - hand side: \(B=180-6x - 9\). Finally, simplify to get \(B=(171 - 6x)^{\circ}\).

Answer:

\((171 - 6x)\)