Question

12 numeric 1 point if arc uv = (8x - 17)° and arc wv = (5x + 52)°, find arc wv. answer previous

Explanation:

Step1: Set up the equation

Since the arcs \(UV\) and \(WV\) are equal (chords are equal, so arcs are equal), we have \(8x - 17=5x + 52\).

Step2: Solve for \(x\)

Subtract \(5x\) from both sides: \(8x-5x - 17=5x-5x + 52\), which simplifies to \(3x-17 = 52\).
Add \(17\) to both sides: \(3x-17 + 17=52 + 17\), so \(3x=69\).
Divide both sides by \(3\): \(x=\frac{69}{3}=23\).

Step3: Find arc \(WV\)

Substitute \(x = 23\) into the expression for arc \(WV\): \(WV=(5x + 52)^{\circ}\).
\(WV=5\times23+52\).
First, calculate \(5\times23 = 115\). Then \(115+52=167\).

Answer:

\(167\)