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:

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

lol

step-by-step explanation: