in the diagram, (mangle fli) is (106^{circ}), (mangle flg=(2x - 1)^{circ}), (mangle glh=(x + 17)^{circ})…

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

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

Answer

Answer:

29°

Explanation:

Step1: Set up an equation

Since (m\angle FLI=m\angle FLG + m\angle GLH+m\angle HLI), we have (106=(2x - 1)+(x + 17)+(4x-15)).

Step2: Simplify the right - hand side

Combine like terms: ((2x - 1)+(x + 17)+(4x-15)=(2x+x + 4x)+(-1 + 17-15)=7x + 1). So the equation becomes (106=7x + 1).

Step3: Solve for (x)

Subtract 1 from both sides: (106-1=7x), so (105 = 7x). Then divide both sides by 7: (x=\frac{105}{7}=15).

Step4: Find the measure of each angle

  • (m\angle FLG=2x - 1=2\times15-1=29^{\circ}).
  • (m\angle GLH=x + 17=15 + 17=32^{\circ}).
  • (m\angle HLI=4x-15=4\times15-15=45^{\circ}).

The smallest angle is (m\angle FLG = 29^{\circ}).