Question

find ( mangle hfg ) if ( mangle 2 = 5x + 13 ) and ( mangle hfg = 13x + 2 ).

Explanation:

Step1: Set up the equation

Since \(\angle2\) and \(\angle1\) form \(\angle HFG\) (assuming \(\angle1=\angle2\) as per angle - bisector or some equal - angle property from the figure's context, if \(\angle HFG=\angle1 + \angle2\) and \(\angle1=\angle2\)), then \(m\angle HFG = 2m\angle2\). Substitute the given expressions: \(13x + 2=2(5x + 13)\).

Step2: Solve the equation

Expand the right - hand side: \(13x + 2 = 10x+26\). Subtract \(10x\) from both sides: \(13x-10x + 2=10x - 10x+26\), which gives \(3x+2 = 26\). Subtract 2 from both sides: \(3x+2 - 2=26 - 2\), so \(3x=24\). Divide both sides by 3: \(x=\frac{24}{3}=8\).

Step3: Find \(m\angle HFG\)

Substitute \(x = 8\) into \(m\angle HFG=13x + 2\). Then \(m\angle HFG=13\times8+2\). Calculate \(13\times8 = 104\), and \(104 + 2=106\).

Answer:

\(106\)