Question

carpentry mr lewis is building a rustic dining table. instead of having four legs, the table has a set of supports at each end. if ∠prq ≅ ∠tvu and m∠rpq = 49°, what is m∠tvu?

Explanation:

Step1: Identify triangle type

Triangles \( \triangle PRQ \) and \( \triangle TVU \) have right angles (at \( Q \) and \( U \)), so they are right triangles.

Step2: Find \( \angle PRQ \)

In right triangle \( \triangle PRQ \), \( m\angle RPQ = 49^\circ \), \( m\angle PQR = 90^\circ \).
Sum of angles in a triangle: \( m\angle PRQ + m\angle RPQ + m\angle PQR = 180^\circ \).
So, \( m\angle PRQ = 180^\circ - 90^\circ - 49^\circ = 41^\circ \).

Step3: Use congruence

Given \( \angle PRQ \cong \angle TVU \), so \( m\angle TVU = m\angle PRQ = 41^\circ \).

Answer:

\( 41^\circ \)