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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:

June 1, 2026Mathematics

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Step-by-step solution

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Here are the solutions for the angles:

4.2.1 $D_3$

Identify parallel lines and transversal.
We are given that $AC \parallel BD$ . $DC$ is a transversal line intersecting these parallel lines.
Apply alternate interior angles theorem.
Since $AC \parallel BD$ , the alternate interior angles $\hat{D}_3$ and $\hat{C}_2$ are equal.
$\hat{D}_3 = \hat{C}_2$ $\hat{D}_3 = 65^\circ \quad (\text{Alternate angles, } AC \parallel BD)$
The size of $D_3$ is $\boxed{\text{65}^\circ}$ .

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