Points a, b, and c divide the circle in a ratio of 1: 3: 14 find the larger angle of the triangle abc
| February 1, 2021 | education
Let the degree measure of the arc AB = X0, then the degree measure of the arc BC = 3 * X0, and the arc AC = 14 * X0.
The degree measure of a full circle is 360, then:
X + 3 * X + 14 * X = 360.
18 * X = 360.
X = 360/18 = 20.
Arc AB = 20, then the inscribed angle ACB = 20/2 = 100.
Arc BC = 3 * 20 = 60, then the inscribed angle BAC = 60/2 = 30.
Arc AC = 14 * 20 = 28, then the inscribed angle ABC = 280/2 = 140.
Answer: The largest angle of triangle ABC is 140.
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