Question

△opq≅△rst by sss. ∠t = 44 degrees, and ∠r = 26 degrees. what is the measure of ∠p? (1 point) degrees

Explanation:

Step1: Recall triangle - angle - sum property

The sum of interior angles of a triangle is 180 degrees. In \(\triangle RST\), we know \(\angle T = 44^{\circ}\) and \(\angle R=26^{\circ}\). Let \(\angle S=x\). Then \(\angle R+\angle S+\angle T = 180^{\circ}\).

Step2: Calculate \(\angle S\)

Substitute the known values into the angle - sum formula: \(26^{\circ}+x + 44^{\circ}=180^{\circ}\). Combine like - terms: \(x=180^{\circ}-(26^{\circ}+44^{\circ})=180^{\circ}-70^{\circ}=110^{\circ}\).

Step3: Use congruence property

Since \(\triangle OPQ\cong\triangle RST\) by SSS (Side - Side - Side congruence), corresponding angles are equal. \(\angle P\) corresponds to \(\angle S\). So \(\angle P=\angle S\).

Answer:

110