Questions: Solve for the missing angle measure. 55° 30° 40° 35°

Solve for the missing angle measure. 55° 30° 40° 35°
Transcript text: Solve for the missing angle measure. $55^{\circ}$ $30^{\circ}$ $40^{\circ}$ $35^{\circ}$
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Solution

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Solution Steps

Step 1: Find the measure of the intercepted arc.

The intercepted arc is given as 290°.

Step 2: Calculate the measure of the missing angle.

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. Therefore, the missing angle is 290°/2 = 145°. However, the diagram shows that the angle is acute, so it must be the supplement of 145°, which is 180° - 145° = 35°.

Final Answer

35°

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