Question

Question 11: A, B, C and D are points on a circle.Angle BAC=40. Angle DBC=55. Find the size of angle DAC

Answer 1

Answer:

55°

Step-by-step explanation:

Angles inscribed in same arc are congrunt

Answer 2

∠ DAC = 125°

Step-by-step explanation:

See the attached diagram.

Here, ACBD is a cyclic quadrilateral with ∠ BAC = 40° and ∠ DBC = 55° {Given}

Now, we have to find the value of ∠ DAC.

Here, being a cyclic quadrilateral ACBD, from its property we can say the sum of the opposite angles of the cyclic quadrilateral ACBD will be 180°.

Hence, ∠ DAC + ∠ DBC = 180°

⇒ ∠ DAC = 180° - ∠ DBC = 180° - 55° = 125° (Answer)