The intersecting chords AB and CD are drawn in the circle. Find the value of the angle DAC, if the measure
| March 4, 2021 | education
The intersecting chords AB and CD are drawn in the circle. Find the value of the angle DAC, if the measure of the angle is ABC = 50 degrees, the measure of the angle is ACD = 40 degrees.
The inscribed angle ACD rests on the arc AD, then the degree measure of the arc AD = 2 * 40 = 80.
The inscribed angle ABC rests on the arc AC, then the degree measure of the arc AC = 2 * 50 = 100.
Then the arc CAD = AD + AC = 80 + 100 = 180.
The sought angle DАС is based on the СВD arc, the degree measure of which is equal to: СВD arc = 360 – СAD = 360 – 180 = 180.
Then the inscribed angle DАС = 180/2 – 90.
Answer: The DAC angle is 90.
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