Question

practice set #4: please be sure to find the measure of each a

1. the m∠ioj=(x + 1)°, m∠jok=(5x - 9)°, m∠iok = 64°. solve for x and find the measure of each angle.

Explanation:

Step1: Set up the equation

Since \(m\angle JOK=(5x - 9)^{\circ}\) and \(m\angle JOK = 64^{\circ}\), we have the equation \(5x-9 = 64\).

Step2: Solve for \(x\)

Add 9 to both sides of the equation: \(5x-9 + 9=64 + 9\), which simplifies to \(5x=73\). Then divide both sides by 5: \(x=\frac{73}{5}=14.6\).

Step3: Find \(m\angle IOJ\)

Substitute \(x = 14.6\) into the expression for \(m\angle IOJ\), so \(m\angle IOJ=(x + 1)^{\circ}=(14.6+1)^{\circ}=15.6^{\circ}\).

Answer:

\(x = 14.6\), \(m\angle IOJ=15.6^{\circ}\), \(m\angle JOK = 64^{\circ}\)