An equilateral triangle LMQ is drawn
in the interior of square LMNP so that side LM is common. Find
m LQP.

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°

LQP = 75 degrees

Step-by-step explanation:

This triangle is an isosceles triangle, LP is equivalent to LQ, and angles LQP and LPQ are also equivalent. We understand that PLQ is equal to 30 degrees, since it's complementary to triangle LQM.

180 - 30 = 150

150/2 = 75.

It'd be helpful if you were to post a picture of the situation, next time though, lol.

Have a nice day, fam. Spread The Love. Thanks for the opportunity.

24+x=y

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form