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°
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