Theorem : 2 Angles in the Same Segment Are Equal

Objective

Understand and apply the theorem that angles in the same segment of a circle are equal
• Identify and solve problems involving equal angles subtended by the same arc
• Use the theorem to justify angle relationships in circle geometry proofs

Definition / Concept

If two angles are subtended by the same arc and lie on the same side of the chord joining the arc’s endpoints, then those angles are equal.

\(\text{In a circle, if arc } AB \text{ subtends } \angle ACB \text{ and } \angle ADB \text{ on the same side of chord } AB,\)

$$\boxed{{\displaystyle \mathrm{\angle }ACB=\mathrm{\angle }AD\mathrm{B<span\; style="font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"></span>}}}$$This is known as the angles in the same segment theorem.

Question

Question

Practice 1: 

Find the value of the angle ‘a’

Practice 2: 

Find the angle ‘b’💡 Show Answer

Practice 3:

Find the angles ‘c’ and  ‘d’

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Practice4:

Find the angle ‘e’

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Practice 5: 

Find the angle ‘f’

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Practice 6: 

Find the angle ‘g’

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Practice 7:

Find the angle ‘h’

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Practice 8: 

A ge

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Practice9: 

Find

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Practice10: 

Find

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