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°

Answer 1

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, $arc(AD)=74\°$

Answer 2

Answer:

74

Step-by-step explanation: