Question

in figure ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A ,B,C,D. If angle ADC = 130 Find angle BAC

Answer 1

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Answer 2

Answer:

Measure of ∠BAC = 40°

Step-by-step explanation:

In the figure attached, there is a circle having AB as the diameter and ∠ADC = 130°

Since angle subtended by the diameter on the circumference of a circle is 90°,

m∠ACB = 90°

Sum of opposite angles of a quadrilateral in a circle is 180°.

Therefore, ∠ADC + ∠CBA = 180°

130° + ∠CBA = 180°

∠CBA = 180 - 130

          = 50°

Now in ΔBAC,

∠BAC + ∠ACB + ∠CBA = 180°

∠BAC + 90°+ 50° = 180°

∠BAC = 180° - 140° = 40°

Therefore, measure of ∠BAC is 40°.

Learn more about the properties of a quadrilateral formed insides the circle from https://brainly.in/question/13950897