Question

1. if $overrightarrow{uw}$ bisects $angle tuv$, $mangle tuw = 13x - 5$ and $mangle wuv = 7x + 31$, find the value of $x$.

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal angles. So, \( m\angle TUW = m\angle WUV \).

Step2: Set Up the Equation

Substitute the given expressions: \( 13x - 5 = 7x + 31 \).

Step3: Solve for \( x \)

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

Answer:

\( x = 6 \)