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

Answer:

mCEA = 90ᴼ because CEA is a right angle, and right angles have 90ᴼ measures.

CEF is a straight angle because there are two 90ᴼ angles (CEA and AEF) and therefore there is 180ᴼ in total. A straight line has a measure of 180ᴼ.

AEF is a right angle because if CEA is a right angle and CEF is a straight line, then AEF has to be a right angle.

Answer 2

The three statements that must be true are:

m∠CEA = 90°

∠CEF is a straight angle

∠AEF is a right angle.

Let's analyze each of the given options using the information given to us and determine whether they are true or not:

• Statement 1: m∠CEA = 90°

The small rectangular sign-shape included in the diagram is used to indicate that a right angle which is 90°.

Therefore, the statement, "m∠CEA = 90°" is TRUE.

• Statement 2: m∠CEF = m∠CEA + m∠BEF

This is FALSE.

m<CEF = m<CEA + AEF NOT m∠CEF = m∠CEA + m∠BEF.

• Statement 3: "m∠CEB = 2(m∠CEA)"

This is also FALSE because,

m<CEB is half of m<CEA since ray EB bisects <CEA.

• Statement 4: "∠CEF is a straight angle."

This is TRUE, because,

m<CEF = m<CEA + m<AEF = 180° (straight line angle = 180°)

• Statement 5: "∠AEF is a right angle."

This is also TRUE because,

m<AEF = 90°

A right angle = 90°

• Therefore, the statements that must be TRUE considering the information given to us are:

m∠CEA = 90°

∠CEF is a straight angle

∠AEF is a right angle.

Learn more about angles here:

https://brainly.com/question/17099436