A puzzle in the form of a quadrilateral is inscribed in a circle. The vertices of the quadrilateral divide the circle into four arcs in a ratio of 1 : 2 : 5 : 4. Find the angle measures of the quadrilateral.

Therefore,

∠A = 30°

∠B = 60°

∠C = 150°

∠D = 120°

Step-by-step explanation:

Given:

A puzzle in the form of a quadrilateral is inscribed in a circle.

The vertices A ,B ,C ,D of the quadrilateral divide the circle into four arcs in a ratio of 1 : 2 : 5 : 4.

Let the common multiple be "x" then the angles will be

∠A = 1x

∠B = 2x

∠C = 5x

∠D = 4x

To Find:

The angle measures of the quadrilateral = ?

Solution:

In a Quadrilateral inscribed in a Circle,

Sum of the measure of all the angles in a Quadrilateral is 360°

Substituting the values we get

Therefore the measures are

∠A = 30°

∠B = 2 × 30 = 60°

∠C = 5 × 30 = 150°

∠D = 4 × 30 = 120°

Therefore,

∠A = 30°

∠B = 60°

∠C = 150°

∠D = 120°

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step-by-step explanation: