Question

consider the figure shown below. find the value of each variable mentioned in the figure below.

b° =

a° =

c° =

Explanation:

Step1: Find \( b^{\circ} \)

The tangent - radius angle is \( 90^{\circ} \).

Step2: Find \( a^{\circ} \)

The measure of an inscribed angle is half the measure of its intercepted arc. The arc measure is \( 52^{\circ} \), so \( a=\frac{52^{\circ}}{2} = 26^{\circ} \).

Step3: Find \( c^{\circ} \)

The measure of an inscribed angle is half the measure of its intercepted arc. The arc measure is \( 84^{\circ} \), so \( c=\frac{84^{\circ}}{2}=42^{\circ} \).

Step4: Verify \( b^{\circ} \)

Since \( b = 90-(a + c) \), substituting \( a = 26^{\circ} \) and \( c = 42^{\circ} \), we get \( b=90-(26 + 42)=22^{\circ} \).

Answer:

\( b = 22^{\circ} \), \( a = 26^{\circ} \), \( c = 42^{\circ} \)