Question

1. angle htn is bisected by (overline{tr}).

a. find the value of ( x ) if ( mangle htr = (7x - 8.5)^circ ) and ( mangle rtn = (5x + 3.5)^circ ).

Explanation:

Step1: Recall angle bisector property

Since \(\overrightarrow{TR}\) bisects \(\angle HTN\), then \(m\angle HTR = m\angle RTN\).
So we set up the equation: \(7x - 8.5 = 5x + 3.5\)

Step2: Solve for \(x\)

Subtract \(5x\) from both sides: \(7x - 5x - 8.5 = 5x - 5x + 3.5\)
Simplify: \(2x - 8.5 = 3.5\)

Add \(8.5\) to both sides: \(2x - 8.5 + 8.5 = 3.5 + 8.5\)
Simplify: \(2x = 12\)

Divide both sides by \(2\): \(\frac{2x}{2} = \frac{12}{2}\)
Simplify: \(x = 6\)

Answer:

\(x = 6\)