Question

in the diagram, \\( \triangle ghj \cong \triangle stu \\).
what are the missing measures in the diagram?
\\( m\angle j = \\)
\\( m\angle t = \\)
\\( m\angle g = \\)
\\( st = \\) cm
\\( hj = \\) cm

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle GHJ\cong\triangle STU\), corresponding angles and sides are equal.

Step2: Find \(m\angle T\)

In \(\triangle GHJ\), using the angle - sum property of a triangle (\(m\angle G + m\angle H+m\angle J=180^{\circ}\)). Given \(m\angle H = 67^{\circ}\), \(m\angle J = 46^{\circ}\), then \(m\angle G=180-(67 + 46)=67^{\circ}\).
Because \(\triangle GHJ\cong\triangle STU\), \(m\angle T=m\angle G = 67^{\circ}\)

Answer:

\(m\angle T = 67^{\circ}\)