Question

if ∠1=(17x + 4)° and ∠2=(20x - 14)°, find m∠1 and m∠2. ∠1 and ∠2 are vertical angles.

Explanation:

Step1: Set up the equation

Since vertical - angles are equal, we set \(17x + 4=20x-14\).

Step2: Solve for \(x\)

Subtract \(17x\) from both sides: \(4 = 20x-17x - 14\), which simplifies to \(4 = 3x-14\). Then add 14 to both sides: \(4 + 14=3x\), so \(18 = 3x\). Divide both sides by 3, we get \(x = 6\).

Step3: Find \(m\angle1\)

Substitute \(x = 6\) into the expression for \(m\angle1=(17x + 4)^{\circ}\). Then \(m\angle1=17\times6 + 4=102 + 4=106^{\circ}\).

Step4: Find \(m\angle2\)

Since \(\angle1\) and \(\angle2\) are vertical - angles, \(m\angle2=m\angle1 = 106^{\circ}\).

Answer:

\(m\angle1 = 106^{\circ}\), \(m\angle2 = 106^{\circ}\)