Question

I’m not to sure on how to find CEB can someone explain how to find it and what the answer would be,please

Answer 1

Answer:

m∠CEB is 55°

Step-by-step explanation:

Since ∠ADE = 55°, and ∠ADE is half of ∠ADC because ED bisects ∠ADC. Bisect means to cut in half.

∠ADC = 110° because it is double of ∠ADE.

Since AB║CD and AD║BC, the two sets of parallel lines means this shape is a parallelogram. In parallelograms, opposite angles have equal measures.

∠ADC = ∠CBE = 110°

All quadrilaterals have a sum of angles 360°. Since ∠DCB = ∠BAD and we know two of these other angles are each 110°:

360° - 2(110°) = 2(∠DCB)

∠DCB = 140°/2

∠DCB = ∠BAD = 70°

∠DCB was bisected by EC, which makes each divided part half.

∠DCE = ∠BCE = (1/2)(∠DCB)

∠DCE = ∠BCE = (1/2)(70°)

∠DCE = ∠BCE = 35°

All triangles' angles sum to 180°.

In ΔBCE, ∠BCE = 35° and ∠CBE = 110°.

∠CEB = 180° - (∠BCE + ∠CBE)

∠CEB = 180° - (35° + 110°)

∠CEB = 55°

Therefore m∠CEB is 55°.