Question

Would appreciate the help.

Answer 1

Answer:

a° = 80° , b° = 40° , c° = 40° , d° = 100°

Step-by-step explanation:

* Lets study the information in the question to solve it

- There is a circle and two chords of it are parallel

∵ The two chords are parallel

- The measure of b° is the same with the angle of measure 40°

   because they are alternate angles

∴ b° = 40°

- The vertex of the angle of measure 40° is on the circle

∴ This angle is inscribed angle subtended by the arc of measure a°

- There is a relation between the inscribed angle and its subtended arc,

 the measure of the arc is twice the measure of the angle

∵ The measure of the angle is 40°

∴ a = 40° × 2 = 80°

∴ a° = 80°

- In the circle any two inscribed angles subtended by the same arc

 are equal in measure

∵ The angle of measure 40° and the angle of measure c° are

  inscribed angles subtended by the same arc of measure a°

∴ c° = 40°

- The sum of the measures of the interior angles in any triangles is 180°

∴ b° + c° + d° = 180° ⇒ interior angles of a Δ

∵ b° = 40° , c° = 40°

∴ 40° + 40° + d° = 180° ⇒ add

∴ 80° + d° = 180° ⇒ subtract 80 from both sides

∴ d° = 100°