Question: In a circle, if two angles subtended by the same arc are equal, what can be concluded about those angles?
Options:
They are complementary
They are equal
They are supplementary
They are proportional
Correct Answer: They are equal
Solution:
Angles subtended by the same arc at the circumference of a circle are equal.
In a circle, if two angles subtended by the same arc are equal, what can be conc
Practice Questions
Q1
In a circle, if two angles subtended by the same arc are equal, what can be concluded about those angles?
They are complementary
They are equal
They are supplementary
They are proportional
Questions & Step-by-Step Solutions
In a circle, if two angles subtended by the same arc are equal, what can be concluded about those angles?
Step 1: Understand what an arc is. An arc is a part of the circumference of a circle.
Step 2: Identify what it means for angles to be subtended by the same arc. This means that both angles are formed by lines that start from the endpoints of the arc and meet at a point on the circle.
Step 3: Visualize the circle with the arc and the angles. Draw a circle and mark two points on the circumference to create an arc.
Step 4: Draw two angles using the endpoints of the arc. Make sure both angles open towards the same arc.
Step 5: Observe that both angles are formed by the same arc. This means they are related to the same section of the circle.
Step 6: Conclude that because both angles are subtended by the same arc, they must be equal.
Angles Subtended by an Arc – In a circle, angles that are subtended by the same arc at the circumference are equal.
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