Question

1. the figure shows a triangle with an angle bisector. if $\angle 2 = 4x + 12$ and $\angle sqr = 11x + 3$. find $x$.

Explanation:

Step1: Use the property of angle bisector

Since \(QP\) is an angle bisector, \(\angle SQR = 2\angle2\).
Given \(\angle2=4x + 12\) and \(\angle SQR=11x + 3\), we substitute into the equation: \(11x+3 = 2(4x + 12)\).

Step2: Expand and solve the equation

Expand \(2(4x + 12)\) using the distributive property \(a(b + c)=ab+ac\), so \(2(4x + 12)=8x+24\).
The equation becomes \(11x + 3=8x+24\).
Subtract \(8x\) from both sides: \(11x-8x + 3=8x-8x+24\), which simplifies to \(3x+3 = 24\).
Subtract \(3\) from both sides: \(3x+3 - 3=24 - 3\), getting \(3x=21\).
Divide both sides by \(3\): \(x=\frac{21}{3}\).

Answer:

\(x = 7\), so the answer is B. 7