Question

Given that ∠CEA is a right angle and (EB) bisects ∠CEA, which statement must be true?

A) ∠BEA ≅ ∠CEA

B) ∠CEB ≅ ∠CEA

C) m∠CEB = 45°

D) m∠CEA = 45°

Answer 1

C) m∠CEB = 45°

Explanation:

A right angle is an angle formed by two perpendicular straight lines, this means that they form an angle of 90º between the two of them, a line bisecting another angle is a line that cuts exactly in half the angle that is bisecting, in this case, the angle is cutting a 90º angle exactly by half, vreating two exact 45º angles whic are CEB and BEA, so the statement that is true from the options is that CEB=45º

Answer 2

The statement is true be option (C) i.e m∠CEB = 45° .

To prove

Reason

As shown in the diagram

∠CEA = ∠CEB + ∠AEB

Bisector

A bisector is that cuts any object into two equal parts

As given

∠CEA is a right angle and EB bisects ∠CEA i.e EB bisect the ∠CEA in the two equal parts .

Thus

`\angle{CEB} = \angle{AEB} = (90^(\circ))/(2)`

∠CEB = ∠AEB = 45 °

Therefore

m ∠CEB = 45 °

Therefore option (C) is correct .

Hence proved