The measure of the ∠LQP is 120°
Step-by-step explanation:
The diagram of the question is as attached in the image.
LMNP is a square. We know that for a square all sides are equal and intersects at 90°
Hence, LM=MP=PN=LN
and ∠LMP= ∠MPN= ∠PNL= ∠NLM= 90°
Δ LMQ is an equilateral triangle
We know that for equilateral triangle all sides are equal and all angles are 60°
LM=LQ=QM=MP=PN=LN and
∠LQM= ∠QML= ∠MLQ= 60°
∠LQP= ∠LQM+ ∠MQP eq 1
In Δ MPQ
∠QPM=90° and ∠PMQ= 90°-60°=30°
Hence, ∠MQP= 180°-(90°+30°)=60°
Putting the value of ∠MQP and ∠LQM in equation 1
∠LQP= 60°+60°= 120°
Thus the measure of ∠LQP=120°
