Question

△omn≅△rpq by the hl theorem. if m∠o = 57 degrees, then what is the measure of ∠p? (1 point) degrees

Explanation:

Step1: Recall congruent - triangle property

Corresponding angles of congruent triangles are equal. Since $\triangle{OMN}\cong\triangle{RPQ}$ by the HL (Hypotenuse - Leg) theorem, $\angle{O}$ and $\angle{R}$ are corresponding angles, and $\angle{M}$ and $\angle{P}$ are corresponding angles.

Step2: Identify right - angled triangles

The triangles are right - angled triangles. We know that in right - angled triangles, if two right - angled triangles are congruent, their corresponding non - right angles are equal.

Step3: Determine the measure of $\angle{P}$

We are given that $m\angle{O}=57^{\circ}$. Since $\triangle{OMN}\cong\triangle{RPQ}$, and $\angle{M}$ and $\angle{P}$ are corresponding angles, and we know that in a right - angled triangle, if we consider the non - right angles, and given the congruence of the triangles, we note that the other non - right angle in $\triangle{OMN}$ (besides the right angle) is $m\angle{M}=90^{\circ}-57^{\circ}=33^{\circ}$. Since $\angle{M}$ and $\angle{P}$ are corresponding angles of congruent triangles, $m\angle{P}=33^{\circ}$.

Answer:

$33$