Question

In the given figure, ΔABC is an equilateral triangle and ABDC is a cyclic
quadrilateral, then find the measure of ∠BDC.

Answer 1

Step-by-step explanation:

since the triangle is equilateral therefore all its angles are of 60°

and quadrilateral ABDC is also cyclic

so angle BAC+BDC=180

60+BDC=180

angle BDC=120°

Answer 2

Given:

• ΔABC is an equilateral triangle.
• ABDC is a cyclic quadrilateral

To Find:

• The measure of the ∠BDC.

Solution:

• From the given data, we get to know that the triangle is equilateral, which means the addition of all the three angles must be equal to 180°
• ⇒ ∠ABC+∠BAC+∠BCA = 180°
• ⇒∠BAC = 60°
• We know that,
• ⇒∠BAC + ∠BDC = 180° (∵ Equilateral triangles)
• So, 60°+∠BDC = 180°
• ⇒∠BDC = 180° - 60°
• ⇒∠BDC = 120°

∴ The measure of ∠BDC = 120°.