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In a trapezium EBCD with EB || DC, find angles a, b, and c given angle CDE = 58 degrees, angle EBC = 110 degrees, and angle BCD = 70 degrees.

Mathematics

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Step-by-step solution

2 steps

Here's how to find the values of angles a, b, and c:

  1. Identify properties of the trapezium EBCDEBCD.

    The arrows on lines EBEB and DCDC indicate that EB∥DCEB \parallel DC. Therefore, EBCDEBCD is a trapezium.
    In a trapezium with parallel sides EBEB and DCDC, the consecutive interior angles between the parallel sides and a transversal are supplementary.
    For transversal EDED: ∠DEB+∠CDE=180∘\angle DEB + \angle CDE = 180^\circ.
    For transversal BCBC: ∠EBC+∠BCD=180∘\angle EBC + \angle BCD = 180^\circ.

  2. Calculate angle b+cb+c.

    Using the transversal EDED:
    $\angle DEB + \

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