In circle E, and are diameters. Angle BCA measures 53°. Circle E is shown. Line segments A C and B D are diameters. Lines are drawn to co

Question

In circle E, and are diameters. Angle BCA measures 53°. Circle E is shown. Line segments A C and B D are diameters. Lines are drawn to connect points B and C and points A and D. Angle B C A is 53 degrees. What is the measure of arc AD? 53° 74° 106° 180°

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1 week 2021-10-08T12:27:44+00:00 2 Answers 0

Answers ( )

    0
    2021-10-08T12:29:13+00:00

    Answer:

    74

    Step-by-step explanation:

    0
    2021-10-08T12:29:35+00:00

    Answer:

    arc(AD)=74\°

    Step-by-step explanation:

    Givens

    • AC and BD are diameters.
    • Angle BCA measures 53°.

    Notice that line segment BE is congruent to line segment CE, because they are the radius of the circumference. That means the triangle that contains these sides is isosceles.

    \angle BCA = 53\° = \angle CBE, by definition of triangles isosceles.

    Then,

    \angle BEC = 180-53-53=74\°, by sum of internal angles.

    And,

    \angle BEC = \angle DEA, by vertical angles definition.

    \angle DEA = 74\°

    But, we know that the measured of a subtended arc is equal to its angle.

    Therefore, arc(AD)=74\°

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