Question

what is the value of x? 82° 83° g x+74° x+41° h k x = ° submit

Explanation:

Step1: Sum of central angles is 360°

The sum of all central angles in a circle is \( 360^\circ \). So we add all the given angles: \( 83^\circ + 82^\circ + (x + 41)^\circ + (x + 74)^\circ = 360^\circ \).

Step2: Simplify the equation

Combine like terms: \( 83 + 82 + 41 + 74 + x + x = 360 \). Calculate the constants: \( 83 + 82 = 165 \), \( 165 + 41 = 206 \), \( 206 + 74 = 280 \). So the equation becomes \( 280 + 2x = 360 \).

Step3: Solve for x

Subtract 280 from both sides: \( 2x = 360 - 280 = 80 \). Then divide by 2: \( x = \frac{80}{2} = 40 \).

Answer:

\( 40 \)