Given: ∆PQR, m∠R = 90° m∠PQR = 75°, m∠MQR = 60° M ∈ PR , MP = 18 Find: RQ

RQ = 9.

Step-by-step explanation:

m < RPQ = 180 - 90 - 75 = 15 degrees

m < PQM = 75 - 60 = 15 degrees.

So triangle PMQ is isosceles so side PM is congruent to side MQ, therefore MQ = 18.

Triangle  RQM is a 30-60-90 triangle with RQ the shortest leg (because it is opposite the lowest angle) so that makes RQ = 1/2 of MQ.  (The sides in a 30-60-90 triangle are in the ratio 1:sqrt3:2)

RQ = 1/2 * 18 = 9.

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9