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 =

Question

Ivanshal

2 months ago

12

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.

Mathematics

2 answers:

Svet_ta [12.7K] · Answer 1 · 2026-03-22T03:14:37+03:00

Answer:

m∠CEA = 90°

m∠BEF = 135°

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

m∠AEF = 90° (∠AEF is a right angle)

Step-by-step explanation:

From the diagram, it is evident that m∠CEA = 90°, given it's indicated to be a right angle (the square in the corner specifies that it measures 90°).

Moreover, m∠CEF = 180°, since if m∠CEA = 90°, m∠AEF = 90° as well, due to their adjacency. Hence, ∠CEF is classified as a straight angle.

Additionally, we can determine that m∠BEF = 135°, since ∠BEF arises from combining ∠BEA + ∠AEF. Knowing m∠AEF = 90°, and knowing ∠BEA represents the bisected angle from the right angle (segment BE bisects that right angle, as shown by the intersection with the small square, dividing it in half). Therefore, m∠BEA = 45°, leading to ∠BEA + ∠AEF = 45° + 90° = 135°

Consequently, the correct findings are:

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

tester [12.3K] · Answer 2 · 2026-03-22T03:17:51+03:00

Answer:

Attached is the question in consideration.

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

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

$\angle CEF$ forms a straight line.

$\angle AEF$ depicts a right triangle.

The options $1,4,5,6$ represent the correct answers.

Step-by-step explanation:

⇒ Given that $\ ray\ AE$ is ⊥ $FEC$ it constitutes a right triangle, leading to $m\angle CEA =90\ (deg)$ .

⇒ The measure for $\angle BEF =135\ (deg)$ equals $\angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg)$ as $\angle AEB$ bisects $\angle AEC$ , implying that $\angle AEB$ is half of $\angle AEC$ , thus $\angle AEB = 45\ (deg)$ .