Question

Points A,B,C,D,E,F lie on a circle in this order (so A between B and F,B between A and C, and so on). Find ∠ABC if ∠CDE=130⁰ and ∠EFA=150⁰

Answer 1

To find ∠ABC, we can use the fact that opposite angles in an inscribed quadrilateral are supplementary. So, ∠ABC + ∠CDE = 180°. Since it is given that ∠CDE = 130°, we can substitute this value: ∠ABC + 130° = 180°. Subtracting 130° from both sides, we find ∠ABC = 50°.

Step-by-step explanation:

To find ∠ABC, we can use the fact that opposite angles in an inscribed quadrilateral are supplementary. So, ∠ABC + ∠CDE = 180°. Since it is given that ∠CDE = 130°, we can substitute this value: ∠ABC + 130° = 180°. Subtracting 130° from both sides, we find ∠ABC = 50°.