In the diagram below, ACDE is a cyclic quadrilateral. BA is a tangent to the circle at A and BD is a tangent to the circle at D. Chords AC, AD, DC and EC are drawn. Furthermore, AC||BD. A1 = 20° and C2 = 65°. Determine, with reasons the sizes of the following angles:

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Asked on June 1, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-06-01T10:38:20.487Z

Here are the solutions for the angles: 4.2.1 D_3 Step 1: Identify parallel lines and transversal. We are given that AC BD. DC is a transversal line intersecting these parallel lines. Step 2: Apply alternate interior angles theorem. Since AC BD, the alternate interior angles D_3 and C_2 are equal. D_3 = C_2 D_3 = 65^ (Alternate angles, AC BD) The size of D_3 is 65^. ** ✂️ _That answer was long and got cut off. Reply continue and I'll finish it._

Accepted Answer · 2026-06-01T10:38:20.487Z

Here are the solutions for the angles: 4.2.1 D_3 Step 1: Identify parallel lines and transversal. We are given that AC BD. DC is a transversal line intersecting these parallel lines. Step 2: Apply alternate interior angles theorem. Since AC BD, the alternate interior angles D_3 and C_2 are equal. D_3 = C_2 D_3 = 65^ (Alternate angles, AC BD) The size of D_3 is 65^. ** ✂️ _That answer was long and got cut off. Reply continue and I'll finish it._

In the diagram below, ACDE is a cyclic quadrilateral. BA is a tangent to the circle at A and BD is a tangent to the circle at D. Chords AC, AD, DC and EC are drawn. Furthermore, AC||BD. A1 = 20° and C2 = 65°. Determine, with reasons the sizes of the following angles:

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In the diagram below, ACDE is a cyclic quadrilateral. BA is a tangent to the circle at A and BD is a tangent to the circle at D. Chords AC, AD, DC and EC are drawn. Furthermore, AC||BD. A1 = 20° and C2 = 65°. Determine, with reasons the sizes of the following angles:

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