Question

Can someone show me how to solve either one of these?

Answer 1

Answer:

x = 2.3

Measure of arc XY = 76° ⇒ answer (D)

Step-by-step explanation:

∵ arc XY congruent to arc YZ

∴ XY = YZ ⇒ chords subtended by equal arcs are equal

∴ 3x = 6.9 ⇒ x = 6.9/3

∴ x = 2.3

In ΔOXY

∵ OX = OY radii

∴ m∠OXY = m∠OYX

∵ m∠OXY = 52°

∴ m∠OYX = 52°

∵ The sum of angles of a Δ = 180°

∴ m∠XOY = 180 - 2 × 52 = 76°

∵ ∠XOY is central angle subtended by arc XY

∴ The measure of arc XY = m∠XOY = 76°