ΔOPQ≅ΔRST

by SSS. ∠T=44
degrees, and ∠R=26
degrees. What is the measure of ∠P
?

1 answer

Since \( \triangle OPQ \cong \triangle RST \) by the Side-Side-Side (SSS) congruence criterion, the corresponding angles of the two triangles are also congruent.

We know that:

  • \( \angle T = 44^\circ \)
  • \( \angle R = 26^\circ \)

To find \( \angle P \), we can first calculate the measure of \( \angle S \) using the fact that the sum of the angles in a triangle is \( 180^\circ \):

For triangle RST: \[ \angle R + \angle S + \angle T = 180^\circ \] Substituting the known values: \[ 26^\circ + \angle S + 44^\circ = 180^\circ \] Combining the known angles: \[ 70^\circ + \angle S = 180^\circ \] Subtracting \( 70^\circ \) from both sides: \[ \angle S = 180^\circ - 70^\circ = 110^\circ \]

Since the triangles are congruent, \( \angle S \) corresponds to \( \angle P \). Thus: \[ \angle P = \angle S = 110^\circ \]

So, the measure of \( \angle P \) is \( \boxed{110^\circ} \).