An equilateral triangle ΔLMQ (see picture to the right) is drawn in the interior of square LMNP so that side LM is common. Find m∠LQP.

The measure of ∠LQP is 120°

Step-by-step explanation:

Since LMNP is a square, it has all its side angles at 90°

Thus ∠LNP= ∠NPM= ∠PML= ∠MLN= 90°

Similarly, all the sides of the square are also equal

Hence, NP=PM=ML=LN

Since Δ LMQ is an equilateral triangle its sides would be equal and all the angle intersecting at 60° angle.

Therefore LM=MQ=LQ

Since LM is one of the square sides, hence the sides of triangle Δ LMQ would be equal to the sides of the square. i.e. LM=MQ=LQ= NP=PM=LN

Now since ∠ LMQ= 60° then ∠ QMP would be 90°-60° = 30

°

In PQM the sum of all the angles would be 180°

Hence, ∠ MQP= 180°-(90°+30°) = 60

°

∠ LQP can be written as ∠ LQM+ ∠ MQP

∠ LQM is 60° and ∠ MQP is 60°

Hence ∠ LQP= 120°

Thus the measure of the ∠ LQP is 120°  

Answer is 75 degrees

Step-by-step explanation:

5050 i think

step-by-step explanation:

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step-by-step explanation: