Triangles \( A B C \) and \( G H J \) are congruent. \( \mathrm{m} \angle A=45^{\circ} . \mathrm{m} \angle B=125^{\circ} \). What are the measurements of \( G H J \) ? A. \( m \angle G=15^{\circ} \) \( m \angle H=125^{\circ} \) \( m \angle J=15^{\circ} \) B. \( m \angle G=15^{\circ} \) \( m \angle H=115^{\circ} \) \( m \angle J=15^{\circ} \) C. \( m \angle G=150^{\circ} \) \( m \angle H=15^{\circ} \) \( m \angle J=15^{\circ} \) D. \( m \angle G=45^{\circ} \) \( m \angle H=125^{\circ} \) D \( m \) B

To find the measurements of triangle \( G H J \), we begin by noting that since triangles \( A B C \) and \( G H J \) are congruent, their corresponding angles must be equal. Given \( m \angle A = 45^{\circ} \) and \( m \angle B = 125^{\circ} \), we can calculate \( m \angle C \) as follows: The sum of the angles in any triangle is \( 180^{\circ} \). So, \[ m \angle C = 180^{\circ} - (m \angle A + m \angle B) = 180^{\circ} - (45^{\circ} + 125^{\circ}) = 180^{\circ} - 170^{\circ} = 10^{\circ}. \] Thus, we have: - \( m \angle A = 45^{\circ} \) - \( m \angle B = 125^{\circ} \) - \( m \angle C = 10^{\circ} \) Consequently, since triangles \( A B C \) and \( G H J \) are congruent, we deduce that: - \( m \angle G = m \angle A = 45^{\circ} \) - \( m \angle H = m \angle B = 125^{\circ} \) - \( m \angle J = m \angle C = 10^{\circ} \) The correct answer is thus \( D \): \( m \angle G = 45^{\circ} \), \( m \angle H = 125^{\circ} \), \( m \angle J = 10^{\circ} \).