ΔOPQ≅ΔRST

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

(1 point)
degrees

1 answer

To find the measure of angle \( ∠P \) in triangle \( ΔOPQ \) based on the congruence \( ΔOPQ ≅ ΔRST \), we can use the fact that corresponding angles in congruent triangles are equal.

Since \( ΔOPQ ≅ ΔRST \):

  • \( ∠R \) in triangle \( RST \) corresponds to \( ∠P \) in triangle \( OPQ \).
  • The measures of \( ∠T \) and \( ∠R \) are given as 44 degrees and 26 degrees, respectively.

First, we need to find the measure of \( ∠S \) in triangle \( RST \). We can use the fact that the sum of interior angles in any triangle is 180 degrees:

\[ ∠R + ∠S + ∠T = 180° \]

Substituting the values we know:

\[ 26° + ∠S + 44° = 180° \]

Now, combine the angles:

\[ 70° + ∠S = 180° \]

Subtract 70° from both sides:

\[ ∠S = 180° - 70° = 110° \]

Now, since \( ΔOPQ ≅ ΔRST \), the angles correspond as follows:

  • \( ∠R \) corresponds to \( ∠P \)
  • \( ∠S \) corresponds to \( ∠Q \)
  • \( ∠T \) corresponds to \( ∠O \)

Since we have already found \( ∠R = 26° \), we conclude that \( ∠P \) is also:

\[ ∠P = ∠R = 26° \]

Thus, the measure of \( ∠P \) is:

\[ \boxed{26} \] degrees.