A puzzle in the form of a quadrilateral is inscribed in a circle. The vertices of the quadrilateral divide the circle into four

Question

musickatia

2 months ago

11

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.

Mathematics

2 answers:

Leona [12.6K] · Answer 1 · 2026-03-20T05:18:08+03:00

Leona [12.6K]2 months ago

7 0

The angles are as follows: m<1=135, m<2=75, m<3=45, and m<4=105. The reasoning is as follows: The total arc measures are given by x+2x+4x+5x=360. Hence, x=30 leads to the respective angle measures calculated from inscribed angles.

Leona [12.6K] · Answer 2 · 2026-03-20T05:20:07+03:00

Consequently, ∠A = 30°, ∠B = 60°, ∠C = 150°, and ∠D = 120°. Step-by-step reasoning: We have a quadrilateral inscribed in a circle. The vertices A, B, C, D create arcs in a ratio of 1:2:5:4. Setting the common multiple as "x", we have ∠A = 1x, ∠B = 2x, ∠C = 5x, ∠D = 4x. To determine the angle measures: in a quadrilateral within a circle, the total angle sum is 360°. Thus, we solve for each angle measure as shown.