Answer:
a° = 118° , b° = 49° , c° = 144° , d° = 98°
Step-by-step explanation:
* Lets study the figure and take the information to solve the question
- There is a circle
- There is an inscribed triangle in the circle
- Each vertex of the triangle is an inscribed angle in the circle
- Each vertex subtended by an arc
- The measure of any inscribed angle is half the measure of its
subtended arc
* Now lets solve the question
- The sum of the measures of the interior angles of a triangle is 180°
∵ The triangle has angle of measure 59° and another angle of
measure 72°
∴ The measure of the third angle = 180° - (59° + 72°) = 49°
∵ b° is the measure of the third angle in the triangle
∴ b° = 49°
- The arc of measure a° is intercept the angle of measure 59°
∵ The measure of the angle is half the measure of the arc
∴ 1/2 a° = 59° ⇒ multiply both sides by 2
∴ a° = 118°
- The arc of measure c° is intercept the angle of measure 72°
∵ The measure of the angle is half the measure of the arc
∴ 1/2 c° = 72° ⇒ multiply both sides by 2
∴ c° = 144°
- The arc of measure d° is intercept the angle of measure 49°
∵ The measure of the angle is half the measure of the arc
∴ 1/2 d° = 49° ⇒ multiply both sides by 2
∴ d° = 98°
using back substitution.