Questions: Given that the arc length of CBE is 176 cm , what is the angle measure of the inscribed angle CDB?

Transcript text: Given that the arc length of CBE is 176 cm , what is the angle measure of the inscribed angle CDB?

Solution

Solution Steps

Step 1: Understand the Problem

We are given the arc length of CBE as 176 cm and need to find the measure of the inscribed angle CDB.

Step 2: Recall the Relationship Between Arc Length and Central Angle

The arc length (s) of a circle is related to the radius (r) and the central angle (θ) in radians by the formula: \[ s = r \theta \]

Step 3: Determine the Central Angle

Since the arc length is given as 176 cm, we need to find the central angle corresponding to this arc. However, the radius is not provided, so we assume the central angle is given directly by the arc length in degrees.

Step 4: Relate Central Angle to Inscribed Angle

The inscribed angle (CDB) is half of the central angle (CBE) that subtends the same arc. Therefore, if the central angle is 176 degrees, the inscribed angle is: \[ \text{Inscribed Angle} = \frac{\text{Central Angle}}{2} = \frac{176^\circ}{2} = 88^\circ \]

Final Answer

The measure of the inscribed angle CDB is \( 88^\circ \).

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