# Quadrangle ABCD is inscribed in a circle. Angle ABC is 82 ° Angle ABD is 47 ° Find angle CAD.

July 23, 2021 | education

| Since the angles ABC and ABD are inscribed in a circle. This means that the degree measure of the arcs is twice as large as the angles themselves.

So the arc AC is equal to:

82 ° * 2 = 164 °,

and the arc AD is equal to:

47 ° * 2 = 94 °,

Then the arc CD is equal to the difference between the arc AC and AD:

164 ° – 94 ° = 70 °,

means the CAD angle is 2 times smaller:

70 °: 2 = 35 °.

Answer: The CAD angle is 35 °.

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