Question

In DEF the measure of D is equal to 5 degrees more than the measure of E. The sum of the measures of D and E is 10 degrees more than the measure of F. Find the measure of each angle.

Answer 1

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

$\Rightarrow\ x+5+x =\text{Angle F}+10\\\\\Rightarrow\ \text{Angle F} = 2x+5-10\\\\\Rightarrow\ \text{Angle F} = 2x-5$

Since DEF is a triangle, so the sum of their angles should equal to 180 degrees.

$\Rightarrow\ x+x+5+2x-5=180\\\\\Rightarrow\ 4x=180\\\\\Rightarrow\ x=45$

Measure of angle E = 45°

Measure of angle D = 45°+5° = 50°

Measure of angle F = (2(45)-5)° = (90-5)° = 85°