Question

if arc uv = (8x - 17)° and arc wv = (5x + 52)°, find arc wv.

Explanation:

Step1: Set arcs equal (congruent chords)

Since the chords from \( V \) to \( U \) and \( V \) to \( W \) are congruent (marked with equal signs), their arcs \( UV \) and \( WV \) are equal. So:
\( 8x - 17 = 5x + 52 \)

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:
\( 3x - 17 = 52 \)
Add 17 to both sides:
\( 3x = 69 \)
Divide by 3:
\( x = 23 \)

Step3: Find arc \( WV \)

Substitute \( x = 23 \) into \( 5x + 52 \):
\( 5(23) + 52 = 115 + 52 = 167 \)

Answer:

\( 167^\circ \)