In △MNO

, m∠M=78°
, m∠N=34°
, and m∠O=68°
. In △RTS
, m∠S=68°
, m∠R=78°
, and m∠T=34°
. Describe the pairs of congruent corresponding angles in the two triangles

1 answer

To determine the pairs of congruent corresponding angles in triangles \( \triangle MNO \) and \( \triangle RTS \), we start by listing the angles in each triangle.

For triangle \( \triangle MNO \):

  • \( m\angle M = 78^\circ \)
  • \( m\angle N = 34^\circ \)
  • \( m\angle O = 68^\circ \)

For triangle \( \triangle RTS \):

  • \( m\angle R = 78^\circ \)
  • \( m\angle S = 68^\circ \)
  • \( m\angle T = 34^\circ \)

Next, we can compare the angles from both triangles:

  • \( m\angle M = 78^\circ \) corresponds to \( m\angle R = 78^\circ \)
  • \( m\angle N = 34^\circ \) corresponds to \( m\angle T = 34^\circ \)
  • \( m\angle O = 68^\circ \) corresponds to \( m\angle S = 68^\circ \)

Therefore, the pairs of congruent corresponding angles in the two triangles are:

  1. \( \angle M \cong \angle R \)
  2. \( \angle N \cong \angle T \)
  3. \( \angle O \cong \angle S \)

In summary, all angles in both triangles are congruent to their corresponding angles in the other triangle.