To find the measure of angle \( \angle P \) in triangle \( \Delta OPQ \), we start by using the fact that the sum of angles in a triangle is \( 180^\circ \).
We know:
- \( \angle T = 44^\circ \)
- \( \angle R = 26^\circ \)
Since the triangles \( \Delta OPQ \) and \( \Delta RST \) are congruent, corresponding angles are equal. Thus, we can use the measures of angles \( \angle R \) and \( \angle T \) to find \( \angle P \).
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First, calculate the measure of \( \angle S \): \[ \angle S = 180^\circ - \angle R - \angle T \] \[ \angle S = 180^\circ - 26^\circ - 44^\circ = 110^\circ \]
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Since \( \angle S \) corresponds to \( \angle P \) in \( \Delta OPQ \), we have: \[ \angle P = \angle S = 110^\circ \]
Thus, the measure of \( \angle P \) is \( 110 \) degrees.