Question

congruence stations. if uw bisects ∠tuv, ( mangle tuw = (13x - 5)^circ ), and ( mangle wuv = (7x + 31)^circ ), find the value of ( x ).

Explanation:

Step1: Use Angle Bisector Definition

Since \( UW \) bisects \( \angle TUV \), \( \angle TUW=\angle WUV \). So, \( 13x - 5=7x + 31 \).

Step2: Solve for \( x \)

Subtract \( 7x \) from both sides: \( 13x-7x - 5=7x-7x + 31 \), which simplifies to \( 6x - 5 = 31 \).
Add 5 to both sides: \( 6x - 5+5 = 31+5 \), so \( 6x = 36 \).
Divide by 6: \( x=\frac{36}{6}=6 \).

Answer:

\( x = 6 \)