Question

use the figure below to answer the following question: if m∠fkh = m∠gkj and m∠fkj = m∠gkh, which of the following conjectures would be true? m∠fkj = m∠fkh points g, k, and h are collinear. ∠gkh forms a linear pair with ∠fkh. points g, k, and j are collinear.

Explanation:

Step1: Analyze angle - equality given

We are given \(m\angle FKH=m\angle GKJ\) and \(m\angle FKJ = m\angle GKH\).

Step2: Analyze collinearity and linear - pair concepts

Collinear points lie on the same straight - line. A linear pair of angles are adjacent angles that form a straight - line (sum to \(180^{\circ}\)).

Step3: Check each conjecture

• For \(m\angle FKJ=m\angle FKH\), there is no information from the given equalities to support this.
• Points \(G\), \(K\), and \(H\) are not collinear as they do not lie on the same straight - line from the figure.
• \(\angle GKH\) and \(\angle FKH\) share a common side \(KH\) and their non - common sides \(KG\) and \(KF\) form a straight - line (\(FG\)). So, \(\angle GKH\) forms a linear pair with \(\angle FKH\).
• Points \(G\), \(K\), and \(J\) are not collinear as they do not lie on the same straight - line from the figure.

Answer:

\(\angle GKH\) forms a linear pair with \(\angle FKH\)