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3 years ago

An equilateral triangle LMQ is drawn

Mathematics

1 answer:

Bogdan [553]3 years ago

5 0

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°

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