Question

what is... 40 x+21 m∠...

Explanation:

Step1: Identify the theorem

This is a problem of angle bisector and perpendicular segments. If a point is on the angle bisector, it is equidistant from the two sides of the angle. So, the lengths of the perpendicular segments from point \( T \) to the two sides of \( \angle V \) are equal.

Step2: Set up the equation

We have \( 4x \) and \( x + 21 \) as the lengths of the perpendicular segments. So, we set them equal: \( 4x=x + 21 \)

Step3: Solve for \( x \)

Subtract \( x \) from both sides: \( 4x-x=x + 21-x \), which simplifies to \( 3x = 21 \). Then divide both sides by 3: \( x=\frac{21}{3}=7 \)

Answer:

\( x = 7 \)