Question 26 of 50beginner⚖️ EvaluateShort Answer2 marks

A cyclic quadrilateral has angles measuring ∠A=80∘\angle A = 80^\circ, ∠B=110∘\angle B = 110^\circ, ∠C=100∘\angle C = 100^\circ, and ∠D=70∘\angle D = 70^\circ. Can such a quadrilateral be drawn? Explain why or why not.

Correct Answer

Yes, such a quadrilateral can be drawn.

Exercise: Exercise | Q: 1 | (Page 22)
For More Understanding

Explanation

The textbook states that in a cyclic quadrilateral, the sum of opposite pairs of angles is 180°. Conversely, if two opposite angles of a quadrilateral add up to 180°, then it is a cyclic quadrilateral. Here, both pairs of opposite angles sum to 180°, satisfying the condition.

Solution Steps

  1. Step 1: Check the sum of opposite angles A and C: 80° + 100° = 180°.

  2. Step 2: Check the sum of opposite angles B and D: 110° + 70° = 180°.

  3. Step 3: Conclude that since both pairs of opposite angles add up to 180°, the quadrilateral can be drawn as a cyclic quadrilateral.

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