Find the angle B of a quadrilateral ABCD inscribed in a circle if ∠B = 2∠D.

Since the quadrilateral given to us is inscribed in a circle, the sum of the values of its opposite angles will be equal to 180 °.

In an inscribed quadrilateral ∠B = 2 * ∠D. We replace ∠D with unknown x, then ∠B will be equal to 2 * x.

Based on these two conditions, you can find the sum of opposite angles, namely аD and ∠B, which will be equal to 180 °. Let’s write it in the form of an equation: x + 2 * x = 180.

Let’s solve this equation by finding x: 3 * x = 180; x = 60.

∠D = 60, therefore, ∠B will be: ∠B = 2 * 60 = 120.

Answer: ∠B = 120.