Question

Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB = 2(m∠CEA) ∠CEF is a straight angle. ∠AEF is a right angle.

Answer 1

m∠CEA = 90°

m∠BEF = 135°

m∠CEF is a straight angle (m∠CEF = 180°)

m∠AEF = 90° (∠AEF is a right angle)

Explanation:

From the image, we see that m∠CEA = 90°, because there's shown that's a right angle (the square in the corner means that is 90°).

Also m∠CEF = 180°, because if m∠CEA = 90°, then m∠AEF = 90° too, because they are adjacent angles. Therefore ∠CEF is a straight angle.

In addition, we deduct that m∠BEF = 135°, because ∠BEF is formed by the sum of ∠BEA + ∠AEF. We know that m∠AEF = 90°, and ∠BEA is the result of the bisection of the right angle (segment BE bisects the right angle, because the graph shoes that the segment crosses that tiny square, dividing it in half). So, m∠BEA = 45°, which gives us ∠BEA + ∠AEF = 45° + 90° = 135°

Therefore, all the right answer would be:

• m∠CEA = 90°
• m∠BEF = 135°
• m∠CEF is a straight angle (m∠CEF = 180°)
• m∠AEF = 90° (∠AEF is a right angle)

Answer 2

Here is the question attached with.

`m\angle CEA =90 \ (deg)`

`m\angle BEF=135\ (deg)`

`\angle CEF` is a straight line.

`\angle AEF` is a right angled triangle.

Options
`1,4,5,6` are correct answers.

Explanation:

⇒As
`\ ray\ AE` is ⊥
`FEC` so it will forms right angled triangle then
`m\angle CEA =90\ (deg)`.

⇒Measure of
`\angle BEF =135\ (deg)` as
`\angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg)` as
`\angle AEB` is the bisector of
`\angle AEC`,meaning that
`\angle AEB` is half of
`\angle AEC` so
`\angle AEB = 45\ (deg)`.

⇒
`\angle CEF` is a straight line as the angles measure over it is
`180\ (deg)`.

⇒Measure of
`\angle AEF = 90\ (deg)` from linear pair concept.

As
`\angle CEA + \angle AEF = 180\ (deg)`,plugging the values of
`m\angle CEA =90\ (deg)` we have
`\angle AEF = 90\ (deg)` .

The other two options are false as:

• 
  `m\angle CEF=m\angle CEA + m\angle BEF = (90+135)=225`

it is exceeding
`180\ (deg)` whereas
`\angle CEF` is a

straight line.

• And
  `m\angle CEB=2(m\angle CEA)` is not true.

As
`\angle CEA = 90\ (deg)` and
`\angle CEB=45\ (deg)`

So we have total
`4` answers.

The correct options are
`1,4,5,6`.