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°

The measure of arc AD is 74°.

Given that,

In circle E, and are diameters. Angle BCA measures 53°. Circle E is shown. Line segments AC and BD are diameters.

Lines are drawn to connect points B and C and points A and D.

Angle BCA is 53 degrees.

We have to determine,

What is the measure of arc AD?

According to the question,

The 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.

Lines are drawn to connect points B and C and points A and D.

Angle BCA is 53 degrees.

By the definition of the isosceles triangle,

∠BCA = 53° =∠CBE

The sum of internal angles is,

∠BEC = 180° - 53° - 53° = 74°

And By vertical angle definition,

∠BEC  = ∠DEA

So, ∠DEA = 74°

The measurement of a subtended arc is equal to its angle is,

Therefore, arc(AD) = 74°

Hence, The measure of arc AD is 74°.

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Step-by-step explanation:

Givens

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.

, by definition of triangles isosceles.

Then,

, by sum of internal angles.

And,

, by vertical angles definition.

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

Therefore,

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.