Quadrilateral ABCD is inscribed in a circle. The angle ABC is 110 degrees and the CAD angle is 69 degrees.
| August 6, 2021 | education
Quadrilateral ABCD is inscribed in a circle. The angle ABC is 110 degrees and the CAD angle is 69 degrees. Find the angle ABD.
The angle ABC is inscribed, rests on the arc ADC and is equal to 110 °, therefore the arc ADC is equal to 220 °.
The CAD angle is inscribed, rests on the DC arc and is 69 °, so the DC arc is 138 °.
Angle ABD is inscribed, rests on the arc AD.
The AD arc is 220 ° – 138 ° = 82 °.
Then the angle ABD is 82 °: 2 = 41 °.
Answer: 41 °.
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