Answer :
Check the picture below.
[tex]\bf \stackrel{\measuredangle D}{D}~~+~~\stackrel{\measuredangle E}{3D}~~+~~\stackrel{\measuredangle F}{E-9}=180~\hfill \implies~\hfill \stackrel{\measuredangle D}{D}~~+~~\stackrel{\measuredangle E}{3D}~~+~~\stackrel{\measuredangle F}{(3D)-9}=180 \\\\\\ 7D-9=180\implies 7D=189\implies D=\cfrac{189}{7}\implies D=27 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle E}{3(27)\implies 81}\qquad \qquad \stackrel{\measuredangle F}{(3D)-9\implies 81-9\implies 72}[/tex]
The measure of the angles are 27°, 72° and 81°.
Based on the information given, the value of each angles will be:
Angle D = d
Angle E = 3 × d = 3d
Angle F = 3d - 9
Sum of angles in a triangle = 180°
Therefore, we'll use the equation below to get the values
d + 3d + 3d - 9 = 180
7d = 180 + 9
7d = 189
d = 189/7
d = 27
Angle D = d = 27
Angle E = 3d = 3 × 27 = 81
Angle F = 3d - 9 = 81 - 9 = 72
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