Question

In circle E, and are diameters. Angle BCA measures 53°. What is the measure of arc AD? °

Answer 1

Question : In circle E, AC and BD are diameters. ∠ BCA measures 53°.
What is the measure of arc AD?

SOLUTION :
FIGURE IS IN THE ATTACHMENT
GIVEN : ∠BCA = 53°
BD and AC are diameters of circle of centre E .
BE = CE (radius)
∠BCE = ∠CBE = 53° [ angle opposite to equal sides are equal]
In ∆ BEC,
∠BEC + ∠BCE + ∠CBE = 180 °
[ANGLE SUM PROPERTY]
∠BEC + 53° + 53° = 180°
∠BEC + 106° = 180°
∠BEC = 180° - 106° = 74°
∠BEC = 74°
Now, angle subtended by arc AD at the Centre is ∠AED
∠AED = ∠BEC = 74°
[Vertically opposite angles]
Hence, angle subtended by arc AD is ∠AED = 74°.

Answer 2

The correct answer is:

74°

The measure of arc AD is 74°.

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