Question

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

∠BEA ≅ ∠CEA
∠CEB ≅ ∠CEA
m∠CEB = 45°
m∠CEA = 45°

Answer 1

m∠CEB = 45° is true.

Explanation:

We are given that,

∠CEA = 90° and BE bisects the ∠CEA.

Since, we know,

'When a line bisects an angle, it divides the angle into two equal parts'

So, we get,

∠CEB = ∠BEA =
`(90)/(2)` = 45°

So, from the options we see that,

Options A, B and D cannot be true. So, only option C is correct.

That is, m∠CEB = 45°

Answer 2

Given that ∠CEA is a right angle which has been bisected by BE, then:
∠CEB=∠BEA
thus each angle will be complementary to each other, hence the size will be:
90/2=45°
hence the correct statement.
m∠CEB = 45°