Question

DE is a chord parallel to diameter AC of the circle with center O . if angleCBD=60, calculate CDE

Answer 1

Question ⤵️

DE is a chord parallel to diameter AC of the circle with center O . if angleCBD=60, calculate CDE.

Answer ⤵️

We know that the angles in the same segment of a circle are equal

From the figure we know that ∠CAD and ∠CBD are in the segment CD

∠CAD=∠CBD=60°

An angle in a semi-circle is a right angle

So we get

∠ADC=90°

Using the angle sum property

∠ACD + ∠ADC + ∠CAD = 180°

By substituting the values

∠ACD+90° +60° = 180°

On further calculation

∠ACD=180° −90° − 60°

By subtraction

ACD = 180° − 150°

So we get

∠ACD=30°

We know that AC∣∣DE and CD is a transversal

From the figure we know that ∠ACD and ∠CDE are alternate angles

So we get

∠CDE=∠ACD=30°

Therefore, ∠CDE=30°

Hope it helps you ✌️

Step-by-step explanation:

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