Question

bt bisects ∠abc. what is the value of x?
diagram: point b with ray ba, ray bt, and another ray; ∠abt is (3x + 13)°, ∠tbc is (5x - 7)°

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, \( \angle ABT = \angle CBT \).

Step2: Set Up Equation

Given \( \angle ABT=(3x + 13)^\circ \) and \( \angle CBT=(5x - 7)^\circ \), we set them equal:
\( 3x + 13 = 5x - 7 \)

Step3: Solve for \( x \)

Subtract \( 3x \) from both sides:
\( 13 = 2x - 7 \)
Add 7 to both sides:
\( 20 = 2x \)
Divide by 2:
\( x = 10 \)

Answer:

\( x = 10 \)