Angle $A$ is circumscribed about circle $O$.
What is the measure of $\angle D$ ?

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the relationship between the inscribed angle and the central angle that subtends the same arc. ‖ ‖ step 2 ⋮ Recognize that angle $A$ is an inscribed angle that subtends arc $BCD$. ‖ ‖ step 3 ⋮ Understand that the central angle $O$ that subtends arc $BCD$ is twice the inscribed angle $A$. ‖ ‖ step 4 ⋮ Calculate the measure of the central angle $O$ using the given measure of angle $A$: $O = 2 imes A = 2 imes 80^\circ = 160^\circ$. ‖ ‖ step 5 ⋮ Note that angle $D$ is also a central angle that subtends arc $BC$. ‖ ‖ step 6 ⋮ Realize that the sum of the central angles $O$ and $D$ that subtend the entire circle must be $360^\circ$. ‖ ‖ step 7 ⋮ Calculate the measure of angle $D$: $D = 360^\circ - O = 360^\circ - 160^\circ = 200^\circ$. ‖ ∻Answer∻ ⚹ The measure of $∠D$ is $200^\circ$. ⚹ ∻Key Concept∻ ⚹Inscribed Angle and Central Angle⚹ ∻Explanation∻ ⚹The inscribed angle is half the measure of the central angle that subtends the same arc. The sum of all central angles in a circle is $360^\circ$.⚹◊What is the relationship between an inscribed angle and a central angle in a circle?⍭ Generate me a similar question◊

Sia