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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Subject:
Mathematics -
Author:
jelly81 -
Created:
7 months ago
Answers 3
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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Author:
gamsj8ox
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Rate an answer:
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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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Author:
hughtyler
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Rate an answer:
5
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