A quadrangle ABCD is inscribed in a circle. The ABD angle is 71 °, the CAD angle is 61 °. Find the angle ABC.
| September 25, 2021 | education
Consider a quadrilateral ABCD, which is inscribed in a circle.
By the condition of the problem, it is known that:
angle ABD = 71 ° and angle CAD = 61 °.
Note that the CAD and CBD corners rest on the same arc. Hence:
angle CAD = angle CBD.
From here we can get:
ABC = ABD + CBD = ABD + CAD = 71 ° + 61 ° = 132 °.
Answer: angle ABC = 132 °.
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