Mathematics

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

1 Answer

  • 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°.

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