Question

in the diagram, m∠fli is 106°, m∠flg = (2x - 1)°, m∠glh = (x + 17)°, and m∠hli = (4x - 15)°. what is the measure of the smallest angle in the diagram? 15° 29° 32° 45°

Explanation:

Step1: Set up angle sum equation

The sum of \( \angle FLG \), \( \angle GLH \), and \( \angle HLI \) equals \( \angle FLI \). So, \((2x - 1)+(x + 17)+(4x - 15)=106\).

Step2: Simplify and solve for \(x\)

Combine like terms: \(2x + x + 4x-1 + 17 - 15 = 106\) → \(7x + 1 = 106\). Subtract 1: \(7x = 105\). Divide by 7: \(x = 15\).

Step3: Calculate each angle

• \( \angle FLG = 2(15)-1 = 29^\circ \)
• \( \angle GLH = 15 + 17 = 32^\circ \)
• \( \angle HLI = 4(15)-15 = 45^\circ \)

Step4: Identify the smallest angle

Compare \(29^\circ\), \(32^\circ\), \(45^\circ\). The smallest is \(29^\circ\).

Answer:

29°