Points A, B, C, D located on a circle divide this circle into four arcs AB, BC, CD and AD

Points A, B, C, D located on a circle divide this circle into four arcs AB, BC, CD and AD, the degree values of which are respectively 1: 5: 10: 20. Find the corner A of quadrilateral ABCD.

The size of the circle is 360 °. According to the condition of the problem, the circle is divided into 4 arcs: 1 + 5 + 10 + 20 = 36 parts, we get that 1 part is 10 °. Let’s write down the degree measure of each arc:
Arc AB = 10 °, arc BC = 50 °, arc CD = 100 °, arc AD = 200 °.
∠ A is the inscribed angle that rests on the arc BD of the given circle.
Degree arc BD = arc BC + arc CD = 50 ° + 100 ° = 150 °.
By the property of the inscribed angle in a circle, we obtain that:
∠ A = 1/2 arc BD = 1/2 * 150 ° = 75 °.
Answer: The degree measure of angle A is 75 °.