780 handshakes.
(n(n-1))/2
(40(40-1))/2
(40*39)/2
1560/2
780
Step-by-step explanation:
1. In PQN & SRT.
a. <RST=<QPN (corresponding angle PQllSR)
b. <STR = <PNQ (corresponding angle TRIINQ)
c. TR=QN (Since TN & QN are opp. Side of parallelogram QNTR)
d. .°.PQN~=SRT.
2.PQN=PSOQ+SNO (whole part axiom)
3.SRT = SNO + NTRO(same as above)
4. PQN=SRT (From st. 1d)
or, PS0Q+SNO =SNO + NTRO (Cancellation of SNO)
or, PS0Q=NTRO
or, PSOQ +QOR=NTRO +QOR (Adding QOR on both side)
or, .°.◼️PQRS = ◼️QRTN
Best of luck!!!!.
Answer: 
<u>Step-by-step explanation:</u>
blue = 8 , red = 6 , green = 4 , total = 18
red and green
x 
=
x 
= 
Answer:
The measures of each would be:
105° and 75°
Step-by-step explanation:
Supplementary angles are two angles whose measures sum up to 180° or they form a straight line.
So if an angle measures 30° less than the measure of its supplementary, it wold mean that both angles together is equal to 180°.
∠1 = x
∠2 = x-30°
∠1 + ∠2 = 180°
So here we plug in our equations:
∠1 + ∠2 = 180°
x + x - 30° = 180°
2x - 30° = 180°
We solve for the x then:
Add 30° on both sides of the equation:
2x - 30° + 30° = 180° + 30°
2x = 210°
Divide both sides by 2:
2x/2 = 210°/2
x = 105°
∠1 = 105°
Now we solve for the second angle:
∠1 + ∠2 = 180°
105° + ∠2 = 180°
Subtract 105° from both sides of the equation:
105° + ∠2 - 105° = 180° - 105°
∠2 = 75°