Question

1. in a triangle, an angle bisector divides the vertex angle into two equal angles, each measuring (2x + 12^circ). if the total vertex angle is (112^circ), what is the value of (x)? options: (28^circ), (24^circ), (22^circ), (18^circ)

Explanation:

Step1: Set up the equation

Since the angle bisector divides the vertex angle into two equal angles, each of measure \(2x + 12\) degrees, the total vertex angle is the sum of these two angles. So we have the equation: \(2(2x + 12)=112\).

Step2: Simplify the left side

First, distribute the 2 on the left side: \(4x + 24 = 112\).

Step3: Solve for x

Subtract 24 from both sides: \(4x=112 - 24\), which simplifies to \(4x = 88\). Then divide both sides by 4: \(x=\frac{88}{4}=22\).

Answer:

22