Question

What is m∠D ? Enter your answer in the box. __°

Answer 1

Check the picture below.

Answer 2

Answer

Find out the m∠D .

To proof

In Δ ABE

∠EAB + ∠ABE + ∠AEB = 180 °

(By using the angle sum property of a triangle.)

As given and shown in the diagram

∠EAB = 14° , ∠ABE = 45 °

Put in the above equation

14° + 45° + ∠AEB = 180 °

∠AEB = 180 °- 59°

∠AEB = 121 °

∠AEB = ∠DEC = 121°

(by using the vertical opposite angles property)

Now in ΔCED

∠DEC + ∠EDC + ∠ECD = 180 °

(Angle sum property of a triangle)

(as given ∠DEC = 121° ,∠ECD = 27° shown in the diagram  )

∠EDC = 180 ° - 27 ° - 121 °

∠EDC  = 32°

therefore

∠ D = 32 °

Hence proved