Question

1. m∠aij = 2x, m∠hia = 60, and m∠hij = 102. find x.

Explanation:

Step1: Identify angle - sum relationship

We know that \(m\angle HIJ=m\angle HIA + m\angle AIJ\).

Step2: Substitute given values

Substitute \(m\angle AIJ = 2x\), \(m\angle HIA=60\), and \(m\angle HIJ = 102\) into the equation: \(102=60 + 2x\).

Step3: Solve for \(x\)

First, subtract 60 from both sides of the equation: \(102−60=2x\), which simplifies to \(42 = 2x\). Then divide both sides by 2: \(x=\frac{42}{2}=21\).

Answer:

21