Answer: Measure of angle E = 45°
Measure of angle D = 45°+5° = 50°
Measure of angle F = 85°
Step-by-step explanation:
Let the measure of angle E be x. ( in degrees)
Then Measure of angle D = x+5
Also, Angle D + Angle E = Angle F +10
[tex]\Rightarrow\ x+5+x =\text{Angle F}+10\\\\\Rightarrow\ \text{Angle F} = 2x+5-10\\\\\Rightarrow\ \text{Angle F} = 2x-5[/tex]
Since DEF is a triangle, so the sum of their angles should equal to 180 degrees.
[tex]\Rightarrow\ x+x+5+2x-5=180\\\\\Rightarrow\ 4x=180\\\\\Rightarrow\ x=45[/tex]
Measure of angle E = 45°
Measure of angle D = 45°+5° = 50°
Measure of angle F = (2(45)-5)° = (90-5)° = 85°
