Right triangles LMN and PQR are similar, where Land M correspond to P and Q, respectively. Angle Mhas a measure of 53°. What is the measure ofangle Q ?

Break Down the Problem

1. We know that triangles LMN and PQR are similar. This means their corresponding angles are equal.
2. We need to determine the measure of angle Q, which corresponds to angle M in triangle LMN.

Relevant Concepts

1. In similar triangles, the angles are congruent. Thus, we can use the measure of angle M to find angle Q.
2. Given that angle M measures 53°, and it corresponds to angle Q, we can conclude that angle Q will have the same measure as angle M due to the property of similar triangles.

Analysis and Detail

1. Since LMN ∼ PQR, we have:
   • Angle L corresponds to angle P
   • Angle M corresponds to angle Q
   • Angle N corresponds to angle R
2. As angle M measures 53°, angle Q, being its corresponding angle, will also measure 53°.

Verify and Summarize

• Since the triangles are similar, the correspondence of the angles confirms that our findings are consistent and accurate.

Final Answer

The measure of angle Q is $53^\circ$.