Question

the sum of the angles of a triangle is 180°. if one angle of a triangle measures x and the second angle measures (3x + 17)°, 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: Set up the equation

Let the third - angle be \(y\). Since the sum of angles in a triangle is \(180^{\circ}\), we have \(x+(3x + 17)+y=180\).

Step2: Solve for \(y\)

First, simplify the left - hand side of the equation: \(x+3x + 17+y=180\), which becomes \(4x+17+y=180\).
Then, isolate \(y\) by subtracting \(4x + 17\) from both sides: \(y=180-(4x + 17)\).

Step3: Simplify the expression for \(y\)

Using the distributive property \(a-(b + c)=a - b - c\), we get \(y=180-4x-17\).
Combine like terms: \(y=(180 - 17)-4x\).
So, \(y = 163-4x\).

Answer:

\((163 - 4x)\)