Question

1. solve for x. circle your answer. diagram: three angles around a point: 214°, 38°, and (x + 3)°; handwritten notes: (x + 3) + 36 + 214, -3 -3, x x -36 + 211 (partial work)

Explanation:

Step1: Sum of angles around a point is 360°

The sum of the angles around a point is \( 360^\circ \). So we have the equation: \( 214^\circ + (x + 3)^\circ + 38^\circ = 360^\circ \)

Step2: Simplify the left - hand side

First, add the known angles: \( 214 + 38=252 \). So the equation becomes \( (x + 3)+252 = 360 \)

Step3: Solve for x

Subtract 252 from both sides: \( x+3=360 - 252 \)
\( x + 3=108 \)
Then subtract 3 from both sides: \( x=108 - 3 \)
\( x = 105 \)

Answer:

\( x = 105 \)